{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Range SLAM with Batch Optimization\n",
    "\n",
    "A 2D Range SLAM example using batch optimization (Levenberg-Marquardt) on the Plaza2 dataset.\n",
    "\n",
    "This notebook mirrors the functionality of the MATLAB batch SLAM script, adapted using Python and GTSAM, drawing structural elements from the iSAM example.\n",
    "\n",
    "Author: Frank Dellaert (adapted for batch by AI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://colab.research.google.com/github/borglab/gtsam/blob/develop/python/gtsam/examples/RangeSLAMExample_plaza2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "GTSAM Copyright 2010-2022, Georgia Tech Research Corporation,\n",
    "Atlanta, Georgia 30332-0415\n",
    "All Rights Reserved\n",
    "\n",
    "Authors: Frank Dellaert, et al. (see THANKS for the full author list)\n",
    "\n",
    "See LICENSE for the license information"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data is second UWB ranging dataset, B2 or \"plaza 2\", from\n",
    "\n",
    "> \"Navigating with Ranging Radios: Five Data Sets with Ground Truth\", by Joseph Djugash, Bradley Hamner, and Stephan Roth, available at https://www.ri.cmu.edu/pub_files/2009/9/Final_5datasetsRangingRadios.pdf\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": [
     "remove-cell"
    ],
    "vscode": {
     "languageId": "markdown"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[31mERROR: Could not find a version that satisfies the requirement gtsam-develop (from versions: none)\u001b[0m\u001b[31m\n",
      "\u001b[0m\u001b[31mERROR: No matching distribution found for gtsam-develop\u001b[0m\u001b[31m\n",
      "\u001b[0mNote: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install --quiet gtsam-develop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pylint: disable=invalid-name, E1101\n",
    "\n",
    "import gtsam\n",
    "from gtsam import Point2, Pose2, symbol\n",
    "import numpy as np\n",
    "import math\n",
    "import time \n",
    "import plotly.express as px\n",
    "\n",
    "from gtsam.utils import plot # Needs matplotlib\n",
    "from numpy.random import default_rng\n",
    "\n",
    "rng = default_rng()\n",
    "\n",
    "NM = gtsam.noiseModel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read 4090 odometry entries.\n"
     ]
    }
   ],
   "source": [
    "# load the odometry\n",
    "# DR: Odometry Input (delta distance traveled and delta heading change)\n",
    "#    Time (sec)  Delta Distance Traveled (m) Delta Heading (rad)\n",
    "odometry_data = {}\n",
    "data_file_dr = gtsam.findExampleDataFile(\"Plaza2_DR.txt\")\n",
    "odo_times_list = []\n",
    "for row in np.loadtxt(data_file_dr):\n",
    "    t, distance_traveled, delta_heading = row\n",
    "    odometry_data[t] = Pose2(distance_traveled, 0, delta_heading)\n",
    "    odo_times_list.append(t)\n",
    "\n",
    "odo_times_list.sort() # Ensure times are sorted\n",
    "M = len(odometry_data)\n",
    "print(f\"Read {M} odometry entries.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Read 1816 range triples for 4 unique landmarks.\n"
     ]
    }
   ],
   "source": [
    "# load the ranges from TD\n",
    "#    Time (sec)  Sender / Antenna ID Receiver Node ID  Range (m)\n",
    "triples = []\n",
    "landmark_ids = set()\n",
    "data_file_td = gtsam.findExampleDataFile(\"Plaza2_TD.txt\")\n",
    "for row in np.loadtxt(data_file_td):\n",
    "    t, sender, receiver, _range = row\n",
    "    landmark_id = int(receiver)\n",
    "    triples.append((t, landmark_id, _range))\n",
    "    landmark_ids.add(landmark_id)\n",
    "\n",
    "K = len(triples)\n",
    "sorted_landmark_ids = sorted(list(landmark_ids))\n",
    "print(f\"Read {K} range triples for {len(landmark_ids)} unique landmarks.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set Parameters and Noise Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "# parameters\n",
    "sigmaR = 50        # range standard deviation (matches MATLAB)\n",
    "sigmaInitialLandmark = 1.0 # Stddev for random landmark init (matches MATLAB)\n",
    "robust = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set Noise parameters (mirrors MATLAB script)\n",
    "priorSigmas = gtsam.Point3(1, 1, math.pi)  # Prior on Pose 0\n",
    "pointPriorSigmas = gtsam.Point2(1, 1) # Loose prior on landmarks\n",
    "odoSigmas = gtsam.Point3(0.05, 0.01, 0.2) # Odometry noise\n",
    "\n",
    "priorNoise = NM.Diagonal.Sigmas(priorSigmas) # prior on pose 0\n",
    "pointPriorNoise = NM.Diagonal.Sigmas(pointPriorSigmas) # loose LM prior\n",
    "odoNoise = NM.Diagonal.Sigmas(odoSigmas)     # odometry\n",
    "\n",
    "# Range noise\n",
    "gaussian = NM.Isotropic.Sigma(1, sigmaR)     # non-robust\n",
    "base = NM.mEstimator.Tukey(15) # Tukey M-estimator like MATLAB\n",
    "tukey = NM.Robust.Create(base, gaussian)  # robust\n",
    "rangeNoise = tukey if robust else gaussian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Build Factor Graph and Initial Estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initializing Landmarks...\n",
      "Initialized 4 landmarks.\n"
     ]
    }
   ],
   "source": [
    "# Initialize Factor Graph and Initial Values\n",
    "graph = gtsam.NonlinearFactorGraph()\n",
    "initial = gtsam.Values()\n",
    "\n",
    "# Add prior on first pose\n",
    "# Estimate pose0 from the first odometry time's neighborhood or use a fixed reasonable guess.\n",
    "# Using the same value as the iSAM example for consistency.\n",
    "pose0 = Pose2(-34.2086489999201, 45.3007639991120, math.pi - 2.021089)\n",
    "graph.add(gtsam.PriorFactorPose2(0, pose0, priorNoise))\n",
    "initial.insert(0, pose0)\n",
    "\n",
    "# Initialize Landmarks (similar to MATLAB approach)\n",
    "print(\"Initializing Landmarks...\")\n",
    "for j in sorted_landmark_ids:\n",
    "    landmark_key = symbol('L', j)\n",
    "    # Initialize randomly around origin (adjust scale if needed)\n",
    "    initial_point = Point2(sigmaInitialLandmark * rng.normal(), sigmaInitialLandmark * rng.normal())\n",
    "    initial.insert(landmark_key, initial_point)\n",
    "    # Optional: Add a loose prior to help localization if landmarks are poorly constrained\n",
    "    # graph.add(gtsam.PriorFactorPoint2(landmark_key, Point2(0,0), pointPriorNoise))\n",
    "print(f\"Initialized {len(sorted_landmark_ids)} landmarks.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Building Pose Chain and Odometry Factors...\n",
      "Added 4090 odometry factors and initial pose estimates.\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nBuilding Pose Chain and Odometry Factors...\")\n",
    "lastPose = pose0\n",
    "pose_times = [odo_times_list[0]] # Approximate time for pose 0\n",
    "# Loop over odometry measurements\n",
    "for i, t in enumerate(odo_times_list, 1):\n",
    "    # get odometry measurement for this time step\n",
    "    odometry = odometry_data[t]\n",
    "\n",
    "    # add odometry factor\n",
    "    graph.add(gtsam.BetweenFactorPose2(i - 1, i, odometry, odoNoise))\n",
    "\n",
    "    # predict pose and add as initial estimate\n",
    "    predictedPose = lastPose.compose(odometry)\n",
    "    lastPose = predictedPose\n",
    "    initial.insert(i, predictedPose)\n",
    "    pose_times.append(t)\n",
    "\n",
    "print(f\"Added {M} odometry factors and initial pose estimates.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Adding Range Factors...\n",
      "Added 1816 range factors.\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nAdding Range Factors...\")\n",
    "# Convert pose_times to numpy array for efficient search\n",
    "pose_times_np = np.array(pose_times)\n",
    "\n",
    "# Add range factors\n",
    "range_factors_added = 0\n",
    "for t_range, landmark_id, measured_range in triples:\n",
    "    # Find the pose index active at the time of the range measurement\n",
    "    # Get the index of the *last* pose time that is <= t_range\n",
    "    pose_index = np.searchsorted(pose_times_np, t_range, side='right') - 1\n",
    "    \n",
    "    # Ensure pose_index is valid (it might be -1 if t_range is before the first odometry time)\n",
    "    if pose_index < 0:\n",
    "        # print(f\"Warning: Range measurement at time {t_range} is before the first pose time {pose_times_np[0]}. Skipping.\")\n",
    "        pose_index = 0 # Or skip the measurement\n",
    "\n",
    "    landmark_key = symbol('L', landmark_id)\n",
    "    graph.add(gtsam.RangeFactor2D(pose_index, landmark_key, measured_range, rangeNoise))\n",
    "    range_factors_added += 1\n",
    "\n",
    "print(f\"Added {range_factors_added} range factors.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimize the Factor Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Optimizing the factor graph...\n",
      "Initial error: 2.9e+02, values: 4095\n",
      "iter      cost      cost_change    lambda  success iter_time\n",
      "   0      1.4e+05     -1.4e+05      1e-05      1       0.03\n",
      "iter      cost      cost_change    lambda  success iter_time\n",
      "   0      9.1e+03     -8.8e+03     0.0001      1       0.03\n",
      "iter      cost      cost_change    lambda  success iter_time\n",
      "   0      1.9e+02        1e+02      0.001      1       0.03\n",
      "   1      2.7e+03     -2.5e+03     0.0001      1       0.03\n",
      "   1      1.1e+02           86      0.001      1       0.02\n",
      "   2      1.7e+03     -1.6e+03     0.0001      1       0.02\n",
      "   2           85           22      0.001      1       0.03\n",
      "   3      6.3e+02     -5.5e+02     0.0001      1       0.03\n",
      "   3           76          8.4      0.001      1       0.02\n",
      "   4      3.1e+02     -2.3e+02     0.0001      1       0.02\n",
      "   4           68          8.6      0.001      1       0.03\n",
      "   5      1.9e+02     -1.2e+02     0.0001      1       0.03\n",
      "   5           55           13      0.001      1       0.03\n",
      "   6      2.6e+02       -2e+02     0.0001      1       0.02\n",
      "   6           39           16      0.001      1       0.02\n",
      "   7      1.4e+02          -99     0.0001      1       0.04\n",
      "   7           26           13      0.001      1       0.03\n",
      "   8           94          -68     0.0001      1       0.03\n",
      "   8           21          5.5      0.001      1       0.03\n",
      "   9           63          -43     0.0001      1       0.02\n",
      "   9           19          2.1      0.001      1       0.02\n",
      "  10           46          -27     0.0001      1       0.02\n",
      "  10           17          1.8      0.001      1       0.03\n",
      "  11           35          -18     0.0001      1       0.03\n",
      "  11           15          1.5      0.001      1       0.03\n",
      "  12           27          -12     0.0001      1       0.03\n",
      "  12           14          1.3      0.001      1       0.02\n",
      "  13           22         -7.9     0.0001      1       0.02\n",
      "  13           13          1.2      0.001      1       0.03\n",
      "  14           18         -5.2     0.0001      1       0.03\n",
      "  14           12            1      0.001      1       0.03\n",
      "  15           15         -3.3     0.0001      1       0.03\n",
      "  15           11          0.9      0.001      1       0.02\n",
      "  16           13           -2     0.0001      1       0.02\n",
      "  16           10         0.79      0.001      1       0.04\n",
      "  17           11         -1.1     0.0001      1       0.03\n",
      "  17          9.3          0.7      0.001      1       0.03\n",
      "  18          9.8        -0.44     0.0001      1       0.03\n",
      "  18          8.7         0.62      0.001      1       0.02\n",
      "  19          8.7        0.023     0.0001      1       0.02\n",
      "  20           67          -58      1e-05      1       0.02\n",
      "  20            5          3.7     0.0001      1       0.03\n",
      "  21           23          -18      1e-05      1       0.03\n",
      "  21          3.5          1.4     0.0001      1       0.03\n",
      "  22          9.4         -5.9      1e-05      1       0.03\n",
      "  22            3         0.57     0.0001      1       0.03\n",
      "  23            5           -2      1e-05      1       0.03\n",
      "  23          2.6         0.34     0.0001      1       0.02\n",
      "  24          3.3        -0.71      1e-05      1       0.02\n",
      "  24          2.4         0.26     0.0001      1       0.03\n",
      "  25          2.6        -0.19      1e-05      1       0.03\n",
      "  25          2.2         0.21     0.0001      1       0.03\n",
      "  26          2.1        0.034      1e-05      1       0.03\n",
      "  27          3.7         -1.5      1e-06      1       0.03\n",
      "  27          1.1            1      1e-05      1       0.02\n",
      "  28          1.4        -0.24      1e-06      1       0.04\n",
      "  28         0.93          0.2      1e-05      1       0.03\n",
      "  29         0.96       -0.031      1e-06      1       0.04\n",
      "  29         0.88        0.048      1e-05      1       0.09\n",
      "  30         0.88      0.00063      1e-06      1       0.03\n",
      "Optimization complete in 1.93 seconds.\n",
      "Initial Error: 294.2927831483431\n",
      "Final Error: 0.8771120075818397\n"
     ]
    }
   ],
   "source": [
    "# Graph built, optimize!\n",
    "print(\"\\nOptimizing the factor graph...\")\n",
    "start_time = time.time()\n",
    "\n",
    "params = gtsam.LevenbergMarquardtParams()\n",
    "params.setRelativeErrorTol(1e-3) # Convergence tolerance\n",
    "params.setVerbosityLM(\"SUMMARY\") # Print LM progress\n",
    "optimizer = gtsam.LevenbergMarquardtOptimizer(graph, initial, params)\n",
    "result = optimizer.optimize()\n",
    "\n",
    "end_time = time.time()\n",
    "print(f\"Optimization complete in {end_time - start_time:.2f} seconds.\")\n",
    "\n",
    "print(f\"Initial Error: {graph.error(initial)}\")\n",
    "print(f\"Final Error: {graph.error(result)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Print and Visualize Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Optimized Landmark Locations:\n",
      "  L0: [-48.11741249  31.92467992]\n",
      "  L1: [-80.92811295  53.95372591]\n",
      "  L5: [-47.60339748 -19.97294509]\n",
      "  L6: [-17.70157972  66.35356579]\n"
     ]
    }
   ],
   "source": [
    "# Print optimized landmarks:\n",
    "print(\"\\nOptimized Landmark Locations:\")\n",
    "for j in [0, 1, 5, 6]: # Print specific landmarks like MATLAB example\n",
    "    if j in sorted_landmark_ids:\n",
    "        landmark_key = gtsam.symbol('L', j)\n",
    "        try:\n",
    "            p = result.atPoint2(landmark_key)\n",
    "            print(f\"  L{j}: {p}\")\n",
    "        except Exception as e:\n",
    "            print(f\"  L{j}: Not found in result ({e})\")\n",
    "    else:\n",
    "        print(f\"  L{j}: Not present in TD data.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Extracted 4091 final poses and 4 landmarks.\n"
     ]
    }
   ],
   "source": [
    "# Extract poses and landmarks for plotting\n",
    "poses_result = gtsam.utilities.allPose2s(result)\n",
    "landmarks_result = gtsam.utilities.extractPoint2(result)\n",
    "positions_result = np.array([poses_result.atPose2(key).translation() \n",
    "                             for key in range(M + 1)]) # Poses 0 to M\n",
    "\n",
    "# Also extract initial estimate poses (dead reckoning)\n",
    "poses_initial = gtsam.utilities.allPose2s(initial)\n",
    "positions_initial = np.array([poses_initial.atPose2(key).translation() \n",
    "                              for key in range(M + 1)])\n",
    "\n",
    "print(f\"\\nExtracted {positions_result.shape[0]} final poses and {landmarks_result.shape[0]} landmarks.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "hovertemplate": "x=%{x}<br>y=%{y}<extra></extra>",
         "legendgroup": "",
         "line": {
          "color": "orange",
          "dash": "dash"
         },
         "marker": {
          "symbol": "circle"
         },
         "mode": "lines",
         "name": "Initial (Odometry)",
         "showlegend": true,
         "type": "scattergl",
         "x": [
          -34.2086489999201,
          -34.20836979114683,
          -34.20803935150894,
          -34.20769664906428,
          -34.20745757618519,
          -34.2072636737919,
          -34.206871418836954,
          -34.20652199326485,
          -34.20607696027076,
          -34.205693383659714,
          -34.20533156377815,
          -34.204892040863555,
          -34.20443556553866,
          -34.20406134318224,
          -34.20369032546497,
          -34.20324242046013,
          -34.2028270923351,
          -34.202401863245235,
          -34.20211269566228,
          -34.20181979427049,
          -34.201513804257694,
          -34.20117029955497,
          -34.20088007284221,
          -34.20055009106879,
          -34.200260116503095,
          -34.19994897517169,
          -34.19965523173816,
          -34.1994029041421,
          -34.19916888715277,
          -34.19891245015342,
          -34.198715504014366,
          -34.198516605035955,
          -34.198300798597955,
          -34.19809721116232,
          -34.197847106023076,
          -34.197616437411,
          -34.19741625511224,
          -34.19724568345311,
          -34.19704074569196,
          -34.196818813999705,
          -34.19666639679551,
          -34.196460828100484,
          -34.19619001400819,
          -34.19604445943367,
          -34.195910099362145,
          -34.195755878773745,
          -34.195558457347744,
          -34.19541386029135,
          -34.19525845476768,
          -34.195067762056134,
          -34.19489202116206,
          -34.194681037789806,
          -34.19447308653113,
          -34.194309983073204,
          -34.194140694618234,
          -34.193972484438326,
          -34.19377363038148,
          -34.19360766124274,
          -34.193492948625305,
          -34.193314314602674,
          -34.19319298281816,
          -34.193028166699094,
          -34.192849816083694,
          -34.192715762273835,
          -34.19257117294791,
          -34.192404794783975,
          -34.19224973021514,
          -34.19189970002379,
          -34.19142560164526,
          -34.19099330407322,
          -34.19057835092971,
          -34.19007616240848,
          -34.18953374612769,
          -34.189050443833295,
          -34.18859249871435,
          -34.18808208875446,
          -34.1875097433046,
          -34.187116421986346,
          -34.186701972454124,
          -34.18624728134878,
          -34.185900489807125,
          -34.18548519298773,
          -34.18497648157919,
          -34.184570210732886,
          -34.18418266111367,
          -34.18366528807,
          -34.183184605808485,
          -34.182655318225876,
          -34.18204098183132,
          -34.181444224279026,
          -34.1808558113075,
          -34.180306857899545,
          -34.17974224332086,
          -34.179135613546975,
          -34.17856989124421,
          -34.178002666401895,
          -34.17746545979827,
          -34.17695023904937,
          -34.17657966394335,
          -34.17624797721639,
          -34.175808057015416,
          -34.17538755257384,
          -34.1750932929447,
          -34.17476769039568,
          -34.174492745418206,
          -34.174075265157256,
          -34.17359930392376,
          -34.173248293211714,
          -34.17282818575748,
          -34.172410770058576,
          -34.17200077254057,
          -34.1715057852681,
          -34.17104567882294,
          -34.170667399995736,
          -34.17025167380646,
          -34.16980106362279,
          -34.16931404150385,
          -34.16882563482927,
          -34.16847743114282,
          -34.16813510653869,
          -34.16769314049209,
          -34.167227624631856,
          -34.166829863331756,
          -34.1664785535197,
          -34.16604401130713,
          -34.165566556343066,
          -34.165109316771826,
          -34.16476249923186,
          -34.16450996370322,
          -34.16408493938013,
          -34.16363029112971,
          -34.163331385529496,
          -34.16296198386089,
          -34.162463869803254,
          -34.16214816634397,
          -34.161631085622886,
          -34.161302187143136,
          -34.16100137657189,
          -34.160822134943274,
          -34.160415997863666,
          -34.159983933185096,
          -34.1597828337861,
          -34.15945735797657,
          -34.159069758030675,
          -34.15866974752631,
          -34.15819360352863,
          -34.1577795637878,
          -34.15746363077512,
          -34.157007863571756,
          -34.156346569946464,
          -34.156033467642835,
          -34.15572418456727,
          -34.15529562345149,
          -34.15483426815585,
          -34.15444066159739,
          -34.15415165343272,
          -34.153924092755815,
          -34.15374222490916,
          -34.15333378170154,
          -34.152980543941716,
          -34.15275576775464,
          -34.15250878222005,
          -34.15210234719164,
          -34.15158887094889,
          -34.150879094911026,
          -34.150549449264666,
          -34.15023150221575,
          -34.14965775724086,
          -34.14878283559801,
          -34.147538049517955,
          -34.14667809897801,
          -34.14597214139117,
          -34.1449514164539,
          -34.14387983516139,
          -34.142902780048296,
          -34.141937345351444,
          -34.14095717101974,
          -34.140035894746084,
          -34.13911887932081,
          -34.138148130768094,
          -34.13724796551392,
          -34.13636077183942,
          -34.135412316421636,
          -34.13442167349488,
          -34.133499345275744,
          -34.132509291074356,
          -34.13151555638633,
          -34.13072016437912,
          -34.13006697028636,
          -34.12932258882978,
          -34.128457114669565,
          -34.12757891903413,
          -34.12675241902658,
          -34.126139745144805,
          -34.125424802483835,
          -34.12458065380563,
          -34.123798126920676,
          -34.123098810690834,
          -34.12257935830928,
          -34.121925358944544,
          -34.12105307672232,
          -34.12049814794496,
          -34.11987641787605,
          -34.119130646124795,
          -34.11816619787505,
          -34.11659424160666,
          -34.115608399386204,
          -34.11412505344007,
          -34.112756498364945,
          -34.11143146952295,
          -34.10740970711347,
          -34.09949525754063,
          -34.085656725623295,
          -34.064029399092696,
          -34.03368048175308,
          -33.99553758936172,
          -33.95340379062459,
          -33.91236348602576,
          -33.87800850917465,
          -33.85056141800388,
          -33.83058697132261,
          -33.81565087648537,
          -33.8049444491882,
          -33.79752120559333,
          -33.79099347717986,
          -33.783043586462696,
          -33.771410205893524,
          -33.75224737940923,
          -33.724723788759974,
          -33.68828786358715,
          -33.64238941373633,
          -33.58724581318574,
          -33.52341612905129,
          -33.45038760071136,
          -33.36755811978665,
          -33.27374271186554,
          -33.16795942535702,
          -33.05070864404693,
          -32.923962785451714,
          -32.78888634928476,
          -32.64315675634603,
          -32.48367840897058,
          -32.31441810159456,
          -32.13596313043152,
          -31.949435410057255,
          -31.75114254781883,
          -31.543629748980248,
          -31.329411925613236,
          -31.09992094177584,
          -30.864274315589554,
          -30.623736251301526,
          -30.367808967460086,
          -30.105392697296736,
          -29.83578637866801,
          -29.56230885492452,
          -29.27975885528539,
          -28.992999595104262,
          -28.71312459191392,
          -28.42724633519638,
          -28.137767487979648,
          -27.851560922928158,
          -27.566770900225954,
          -27.278683483004144,
          -26.99787632255226,
          -26.724396432763083,
          -26.455175707897624,
          -26.188565191864626,
          -25.930075902409982,
          -25.689501249129936,
          -25.448340743431032,
          -25.211526485546386,
          -25.009803441735496,
          -24.807447165750766,
          -24.610989417765634,
          -24.42995646453449,
          -24.257893036665816,
          -24.0962655892048,
          -23.939813766971866,
          -23.785188463141555,
          -23.64708304417443,
          -23.512520266968043,
          -23.376751262029757,
          -23.254752370972582,
          -23.13742752911834,
          -23.01995921198726,
          -22.910574875820885,
          -22.809344622794356,
          -22.71317181234873,
          -22.619507532029218,
          -22.531519207941866,
          -22.449978646212163,
          -22.373832177497228,
          -22.304127240580957,
          -22.23823689915115,
          -22.17693091756414,
          -22.124225918965703,
          -22.07695602632899,
          -22.031931398110828,
          -21.989307820101615,
          -21.950083211647588,
          -21.910462943189394,
          -21.867609092975304,
          -21.82625754897879,
          -21.78646587326728,
          -21.746208522646977,
          -21.705243463354428,
          -21.667515584399062,
          -21.62887810665828,
          -21.586339021035123,
          -21.54498217834841,
          -21.50613878979132,
          -21.46468713528134,
          -21.422628128270116,
          -21.381494411838712,
          -21.338363098912186,
          -21.295671232801663,
          -21.2517648377332,
          -21.209440777853917,
          -21.16629088618545,
          -21.12212193411109,
          -21.079305963402135,
          -21.035026940876488,
          -20.988806156340544,
          -20.938972364221645,
          -20.890580380571773,
          -20.840388844467203,
          -20.78615161846691,
          -20.729836241071755,
          -20.670402780757634,
          -20.609787505781618,
          -20.546402957679422,
          -20.480120171609556,
          -20.41198830792046,
          -20.341235516317333,
          -20.268538456087622,
          -20.194194955267772,
          -20.117301900801706,
          -20.036731061186252,
          -19.95468505013031,
          -19.868699134763833,
          -19.77462426493531,
          -19.67986282301832,
          -19.581995761257062,
          -19.47466325395279,
          -19.36273362009527,
          -19.248791232362585,
          -19.12450696171867,
          -18.995796013658993,
          -18.862174198065357,
          -18.72074076298342,
          -18.576806843799996,
          -18.4249629947287,
          -18.262822742914462,
          -18.098040162588983,
          -17.92699900601009,
          -17.743514170132606,
          -17.560493449686934,
          -17.372015377233666,
          -17.17238149097355,
          -16.97541110912954,
          -16.776237703761932,
          -16.568977338492545,
          -16.36389486671192,
          -16.159994671884743,
          -15.947954387898216,
          -15.735828175092163,
          -15.530840738447175,
          -15.322367537110173,
          -15.114473275527201,
          -14.908864616675404,
          -14.703632643001981,
          -14.493620207990459,
          -14.283429922868448,
          -14.073735470071078,
          -13.864882478884011,
          -13.653542855632638,
          -13.446157017298724,
          -13.240450308445956,
          -13.03254888534216,
          -12.82879238721366,
          -12.625931022837921,
          -12.420423880877294,
          -12.218858416409285,
          -12.022165537372443,
          -11.825676906596087,
          -11.634856193821676,
          -11.451732356842388,
          -11.247230541528497,
          -11.060952984643725,
          -10.880935755346197,
          -10.702858414999122,
          -10.525433949694676,
          -10.351124648376633,
          -10.181752064538339,
          -10.012534030906886,
          -9.848038552982812,
          -9.686901678027139,
          -9.526765307236076,
          -9.371758097898878,
          -9.215264971070289,
          -9.059261042177,
          -8.906756953593783,
          -8.755843071943021,
          -8.605294735699728,
          -8.463275783481409,
          -8.329190931335454,
          -8.19369233294814,
          -8.0692156189969,
          -7.957216438928777,
          -7.847220752904937,
          -7.747069786469661,
          -7.660310444789812,
          -7.579305780836443,
          -7.509036127875443,
          -7.452017387410774,
          -7.405222753283836,
          -7.372073035485067,
          -7.351642614806359,
          -7.343177466094715,
          -7.347361197476441,
          -7.365735556099691,
          -7.399156885256334,
          -7.445360657763755,
          -7.508776765471713,
          -7.5927583213542436,
          -7.691455380855894,
          -7.807186907221394,
          -7.940512252030794,
          -8.093125828074614,
          -8.269604259222355,
          -8.473507609030213,
          -8.684597260765347,
          -8.90762400264664,
          -9.158369270369137,
          -9.414517782519223,
          -9.676485984615962,
          -9.969182915609869,
          -10.266655713459462,
          -10.55807520953602,
          -10.866789682755009,
          -11.18402793906773,
          -11.502005862565333,
          -11.825750159204869,
          -12.149457350470596,
          -12.471233265292803,
          -12.798585381492586,
          -13.122099173279063,
          -13.443047334476752,
          -13.76471032475758,
          -14.083597315288468,
          -14.398595030817017,
          -14.715489513179412,
          -15.024865561808635,
          -15.33263427801308,
          -15.640571566341688,
          -15.941612412184652,
          -16.24040289031909,
          -16.539924732517363,
          -16.83590412247988,
          -17.131319977153872,
          -17.428339650906224,
          -17.72867730697316,
          -18.029332598697753,
          -18.33273157445459,
          -18.638847939348018,
          -18.949488962162466,
          -19.26412009371686,
          -19.586822101861458,
          -19.923017274196553,
          -20.261872661811843,
          -20.603947245474316,
          -20.958966844932917,
          -21.314551872621777,
          -21.667166798469715,
          -22.032699596753904,
          -22.411522053759192,
          -22.776362008833686,
          -23.15208156156842,
          -23.546676852918527,
          -23.92067875520956,
          -24.308761843228947,
          -24.71190798064512,
          -25.09792435154741,
          -25.497564826276022,
          -25.90868675985076,
          -26.29742349166464,
          -26.694454583952325,
          -27.099808943673086,
          -27.47666241999062,
          -27.855645950507423,
          -28.260841892246933,
          -28.65141831699363,
          -29.02798499263422,
          -29.429967515377168,
          -29.828877112257004,
          -30.20623374775589,
          -30.60346100788182,
          -31.00593668328393,
          -31.39048611841581,
          -31.782926405143584,
          -32.17868413738589,
          -32.55977264296768,
          -32.94512410748157,
          -33.330915742264054,
          -33.712635519621315,
          -34.097676707286155,
          -34.482474934446415,
          -34.86477834110895,
          -35.25316252077966,
          -35.63979801719962,
          -36.02925966667758,
          -36.42024268506567,
          -36.81612541766959,
          -37.208494830948204,
          -37.59953258183762,
          -37.98948836224458,
          -38.373589535086744,
          -38.749522301219656,
          -39.124013397388076,
          -39.49760288322387,
          -39.87450057054848,
          -40.258518113709755,
          -40.648739126828815,
          -41.03870038319137,
          -41.42704450655007,
          -41.81274057712025,
          -42.19515301354295,
          -42.58488833284426,
          -42.97668394398382,
          -43.364210178023065,
          -43.739919223387076,
          -44.11079386997858,
          -44.48257316394245,
          -44.85321160432007,
          -45.22495996659519,
          -45.59262925672443,
          -45.96279446238195,
          -46.33399343312924,
          -46.69162151604925,
          -47.05013773412914,
          -47.41892127042934,
          -47.77831689057106,
          -48.136030253455665,
          -48.49888236769298,
          -48.86349611699248,
          -49.22108678260273,
          -49.57570642648424,
          -49.92947036109773,
          -50.274706538797254,
          -50.614965488147575,
          -50.964947802491984,
          -51.309516044623926,
          -51.64395595262953,
          -51.98688538713852,
          -52.325034614501384,
          -52.64536286364738,
          -52.97776600605042,
          -53.305485485769815,
          -53.622106066193076,
          -53.951384822826775,
          -54.28100594529425,
          -54.59527919871606,
          -54.92252186474323,
          -55.2477175995997,
          -55.560303894522775,
          -55.88723007893267,
          -56.20939312176507,
          -56.517615020186284,
          -56.83462644280102,
          -57.14058455681063,
          -57.44433310644948,
          -57.755042297251784,
          -58.06127286099091,
          -58.365787223773054,
          -58.67240778062577,
          -58.97278734814268,
          -59.27134758243663,
          -59.57953972712718,
          -59.87675130379625,
          -60.17840020009142,
          -60.479121813545,
          -60.76066281110613,
          -61.04257603044654,
          -61.32028234240231,
          -61.571288303886206,
          -61.82421304542558,
          -62.07176949083373,
          -62.29703239472938,
          -62.514855841875956,
          -62.72351165643634,
          -62.91782612832176,
          -63.09626044458709,
          -63.265265498296955,
          -63.42286360637691,
          -63.566943502258184,
          -63.700676684767984,
          -63.82163068824623,
          -63.93594093491176,
          -64.04396315960943,
          -64.1399152615282,
          -64.22602688025769,
          -64.3032687295051,
          -64.37286672176609,
          -64.4351265593657,
          -64.48754224501491,
          -64.53452306913441,
          -64.57779542218493,
          -64.61262474702409,
          -64.63642641850628,
          -64.65019798608247,
          -64.65498179041354,
          -64.6497146978355,
          -64.6326206448963,
          -64.60518713668186,
          -64.56885384104137,
          -64.52097117513405,
          -64.45955652984058,
          -64.38451814775523,
          -64.29060293682289,
          -64.17992812807096,
          -64.05966390630117,
          -63.925508546901916,
          -63.77516028982094,
          -63.61034033759696,
          -63.4293737384692,
          -63.23581452479093,
          -63.031021619411845,
          -62.81225115151607,
          -62.583839788194865,
          -62.34866864499496,
          -62.09789634574366,
          -61.83290019315182,
          -61.56162483680962,
          -61.28536659815268,
          -60.99522104250729,
          -60.69968775906392,
          -60.42085119471336,
          -60.1283188169592,
          -59.819008645838885,
          -59.53076491571798,
          -59.23751466372139,
          -58.91497230190822,
          -58.60748762278332,
          -58.30400734584279,
          -57.97467245220812,
          -57.654106742048384,
          -57.33625888903485,
          -57.00259227257815,
          -56.674841483157955,
          -56.35305374687847,
          -56.02553718554206,
          -55.702262112283556,
          -55.3814721540694,
          -55.05688954508452,
          -54.73009699822438,
          -54.406255577449514,
          -54.08167634282728,
          -53.76221867258252,
          -53.44485768106943,
          -53.13219728048551,
          -52.81457574298221,
          -52.503015569422374,
          -52.189251770484056,
          -51.87343074646113,
          -51.56389404627859,
          -51.26344155270778,
          -50.95358319162299,
          -50.66424018599097,
          -50.384498177485725,
          -50.09160927167098,
          -49.812435968513945,
          -49.532124266908106,
          -49.238984228217916,
          -48.95738046395134,
          -48.67661571585529,
          -48.35937981335118,
          -48.076640185916744,
          -47.79767229534073,
          -47.50863977716664,
          -47.21210993114214,
          -46.9237025968253,
          -46.634090376746094,
          -46.336014867755594,
          -46.04330953357996,
          -45.75715272138405,
          -45.46276075279872,
          -45.16733514294459,
          -44.87774275444449,
          -44.58033268485854,
          -44.28107050649222,
          -43.99194096366448,
          -43.70134796782298,
          -43.412659024856765,
          -43.13559484747741,
          -42.85286754474855,
          -42.574171057790586,
          -42.2980238735172,
          -42.01551175653316,
          -41.72762840582466,
          -41.433042978584986,
          -41.14015786685668,
          -40.84172003708187,
          -40.53104176574113,
          -40.213813602199096,
          -39.89309565909701,
          -39.57014806376517,
          -39.244171495856754,
          -38.915987784882,
          -38.58934801406164,
          -38.272128932215665,
          -37.9574687989562,
          -37.63743254921885,
          -37.32073864769026,
          -37.00818203440748,
          -36.68917419502268,
          -36.366818137408664,
          -36.04611012514127,
          -35.72653438453104,
          -35.408492517158194,
          -35.073714926966915,
          -34.746377234386735,
          -34.42955066989188,
          -34.09223102852332,
          -33.75484965456418,
          -33.445829076672325,
          -33.11552897191394,
          -32.77037994873269,
          -32.44992703279743,
          -32.12502826021245,
          -31.778207451202064,
          -31.447701203771487,
          -31.14246155537935,
          -30.80809149890923,
          -30.466156203951886,
          -30.14728339242797,
          -29.807374072655794,
          -29.45731418587252,
          -29.12235329034721,
          -28.776342357177302,
          -28.432661774193978,
          -28.093522680701145,
          -27.75150758606779,
          -27.40818939678314,
          -27.07608526011534,
          -26.737157023012063,
          -26.406410594476682,
          -26.08971609110852,
          -25.75672148863116,
          -25.423141857524186,
          -25.105838163229688,
          -24.787731148602155,
          -24.46920132865978,
          -24.159634778771718,
          -23.86297868393125,
          -23.566174282178487,
          -23.28606418943286,
          -23.022583879609392,
          -22.761391232675397,
          -22.5071206699873,
          -22.27328754880599,
          -22.042892722522282,
          -21.816476176435494,
          -21.605541375580295,
          -21.39690581411838,
          -21.20139429916033,
          -21.018535678533095,
          -20.842962364245956,
          -20.681382851286852,
          -20.53259405197908,
          -20.395943983475348,
          -20.270092149571834,
          -20.15678453921385,
          -20.054496019842436,
          -19.96021401192574,
          -19.87451420907953,
          -19.796616008695267,
          -19.72654075407966,
          -19.664238258442694,
          -19.6070255660196,
          -19.555416051879025,
          -19.510398075787894,
          -19.47009575583654,
          -19.43334999192826,
          -19.400534848988084,
          -19.369130813601668,
          -19.339743557596968,
          -19.313852629320575,
          -19.28879200496297,
          -19.263592162642702,
          -19.241102160584422,
          -19.220401767732763,
          -19.19955127727777,
          -19.17789277396974,
          -19.157745103413344,
          -19.13944712783892,
          -19.12140771540347,
          -19.104128716144565,
          -19.087530801150898,
          -19.071959241824285,
          -19.056826020635853,
          -19.041259733635773,
          -19.025089282415408,
          -19.008470458905915,
          -18.992073479289715,
          -18.975470727857175,
          -18.958654544359934,
          -18.94150962275529,
          -18.923880162808086,
          -18.905630551124812,
          -18.88867845388129,
          -18.87195186841717,
          -18.855656173513683,
          -18.838576376643513,
          -18.821760920458527,
          -18.80507873057346,
          -18.786936283588805,
          -18.768366418163772,
          -18.751573547862648,
          -18.7356535042555,
          -18.721027682078418,
          -18.708265908634843,
          -18.697327682769227,
          -18.68811769529859,
          -18.682554474080927,
          -18.680346272120985,
          -18.680177332852963,
          -18.68265591665324,
          -18.69014605814047,
          -18.701475586703168,
          -18.71521800274297,
          -18.732826158150633,
          -18.75601256492638,
          -18.78365036264507,
          -18.8154452722153,
          -18.852149822657232,
          -18.89369469436917,
          -18.934430685455094,
          -18.977897048149778,
          -19.02228713257116,
          -19.066346439718593,
          -19.111481910157305,
          -19.157756815679925,
          -19.2043070603169,
          -19.249380310411922,
          -19.295460499803077,
          -19.3393994393193,
          -19.38141214866904,
          -19.425552390510045,
          -19.473016557213317,
          -19.52186987369341,
          -19.569739838061423,
          -19.61794840606325,
          -19.6679099624962,
          -19.71844726490396,
          -19.771637738164948,
          -19.82470445124085,
          -19.879312172256398,
          -19.934177990580114,
          -19.986597680985927,
          -20.039480863754484,
          -20.09230662741227,
          -20.14534830578189,
          -20.19798657030222,
          -20.251622289749257,
          -20.306095188670973,
          -20.363846306660687,
          -20.414516043851275,
          -20.465518298521012,
          -20.515465566980836,
          -20.561836183562683,
          -20.603053318393517,
          -20.641846957654924,
          -20.67675711657683,
          -20.707382977366915,
          -20.733585257799767,
          -20.754546746502523,
          -20.769722502433204,
          -20.77746589489218,
          -20.779074056307735,
          -20.774396629799046,
          -20.764224608688664,
          -20.75026863278645,
          -20.732003495366133,
          -20.710344145930513,
          -20.68469101797568,
          -20.654597128865635,
          -20.622065177647716,
          -20.58665237991359,
          -20.5454917546794,
          -20.5009018255594,
          -20.453813816927212,
          -20.3999210465216,
          -20.34278601093995,
          -20.284286124896127,
          -20.218975731612954,
          -20.152708559242253,
          -20.088978293827637,
          -20.01323095299503,
          -19.939426652328745,
          -19.86739686010645,
          -19.79247723956603,
          -19.708606351768413,
          -19.626406400347683,
          -19.54240362614865,
          -19.453693918647424,
          -19.365521774108203,
          -19.27650134867682,
          -19.18510298124001,
          -19.09212417154239,
          -18.997033635222746,
          -18.900438430035134,
          -18.802858904701715,
          -18.702046619281894,
          -18.598910212516117,
          -18.495508656721444,
          -18.39072501995874,
          -18.28447531955079,
          -18.178582345736874,
          -18.076410428925655,
          -17.97165282444552,
          -17.86765844756164,
          -17.76545154440105,
          -17.661242458286257,
          -17.557836728725114,
          -17.454912303802896,
          -17.353945706767032,
          -17.25537006259427,
          -17.160229526963754,
          -17.065919351409473,
          -16.971618903822495,
          -16.878661620156794,
          -16.78779282169796,
          -16.698497862155378,
          -16.61077079014498,
          -16.525904850869782,
          -16.442780550088887,
          -16.360498988663544,
          -16.281534726796973,
          -16.206802340143952,
          -16.133778928416323,
          -16.062264166852707,
          -15.993049059317531,
          -15.92822979090142,
          -15.863879618921702,
          -15.799875703306611,
          -15.736119217937642,
          -15.674630374813349,
          -15.614840434623366,
          -15.547444349619692,
          -15.487395638825438,
          -15.432527121648045,
          -15.381583812586285,
          -15.334598123540111,
          -15.293450115453636,
          -15.259856994555934,
          -15.233690619946962,
          -15.21494153246387,
          -15.203634558837665,
          -15.201154380910786,
          -15.209078670416062,
          -15.225359092081764,
          -15.250002036936612,
          -15.284649538139242,
          -15.327522593153994,
          -15.380709985912155,
          -15.44573848269761,
          -15.519353051247695,
          -15.604559990183146,
          -15.702240879132068,
          -15.811527701771865,
          -15.933654783769107,
          -16.071140021074356,
          -16.221391811186244,
          -16.389188603052308,
          -16.570479788727262,
          -16.764117128990062,
          -16.9692948221372,
          -17.189413386956197,
          -17.432762157106843,
          -17.681107670345288,
          -17.932541135233734,
          -18.21091660629076,
          -18.498191364237368,
          -18.78330636844814,
          -19.08406975623124,
          -19.393422112588933,
          -19.698910108159087,
          -20.01584816113684,
          -20.33382844384227,
          -20.64163741949853,
          -20.955675612409408,
          -21.2687763371419,
          -21.566485067367573,
          -21.859561974408624,
          -22.1502341727436,
          -22.42348529997479,
          -22.69551795661861,
          -22.96438927676706,
          -23.215573834652048,
          -23.46244839926611,
          -23.704584665809353,
          -23.930505606997098,
          -24.150451705189653,
          -24.365190008980353,
          -24.5699314676053,
          -24.76780132169323,
          -24.9620925332786,
          -25.152068297062918,
          -25.336977122245695,
          -25.520267517466507,
          -25.702857737051826,
          -25.886034594401092,
          -26.07282477580728,
          -26.263584887429488,
          -26.46099862005774,
          -26.661902468778145,
          -26.866393400065217,
          -27.075049483206225,
          -27.285808865637744,
          -27.50052801073749,
          -27.71933669622049,
          -27.941760780363364,
          -28.171142171861774,
          -28.403646992785575,
          -28.63741550040471,
          -28.88240210565768,
          -29.12706791493376,
          -29.372781377653563,
          -29.62024863079779,
          -29.88034754011355,
          -30.14178729354976,
          -30.396276067264644,
          -30.669073320253485,
          -30.946319514409478,
          -31.21186178660606,
          -31.488190575329675,
          -31.779675322644817,
          -32.06103461148627,
          -32.34824070984298,
          -32.65050665257917,
          -32.9430373739719,
          -33.23319583733999,
          -33.535798533110025,
          -33.83685624268183,
          -34.13320508363247,
          -34.4353164638501,
          -34.744494359853,
          -35.05140883901183,
          -35.3582604085396,
          -35.66826458626864,
          -35.983572628096425,
          -36.294097318226406,
          -36.605853544426914,
          -36.926992330684705,
          -37.24610367189432,
          -37.560138397490675,
          -37.87888945497262,
          -38.20281110243761,
          -38.51529346900825,
          -38.82348631293479,
          -39.1382453334092,
          -39.44136154185805,
          -39.74276489287358,
          -40.04702673125926,
          -40.34663653188699,
          -40.64638782270767,
          -40.94445094060477,
          -41.23703448331536,
          -41.53229260851288,
          -41.830827041690725,
          -42.12370450766311,
          -42.416638243414454,
          -42.709962427881,
          -42.99753716100533,
          -43.282364958524965,
          -43.56671769411638,
          -43.84306194611597,
          -44.111269220469495,
          -44.38328890038548,
          -44.645007505848994,
          -44.906834025243484,
          -45.17353352395579,
          -45.439187669545255,
          -45.70266112832891,
          -45.97349090158788,
          -46.24170051178181,
          -46.501858146120476,
          -46.76200338762441,
          -47.02328154783815,
          -47.27692660393374,
          -47.53078240405272,
          -47.78599818368028,
          -48.03098356520449,
          -48.26909335009252,
          -48.5082370295951,
          -48.745697031594425,
          -48.97781630309095,
          -49.21609489615746,
          -49.453754710454845,
          -49.684993713303136,
          -49.91756206913763,
          -50.14892747822964,
          -50.37055342338956,
          -50.59324272015816,
          -50.816585275357596,
          -51.03522073520233,
          -51.24834950164259,
          -51.46127850930465,
          -51.673863210934066,
          -51.88460858481911,
          -52.09273802026191,
          -52.30054630881307,
          -52.50850356230636,
          -52.71424803446304,
          -52.917419956162234,
          -53.122994929547055,
          -53.3309545468346,
          -53.53399739045991,
          -53.73599752841803,
          -53.939986289299156,
          -54.140533778272065,
          -54.332037144773864,
          -54.52668695660694,
          -54.72146496905921,
          -54.90905918977328,
          -55.0981800450627,
          -55.29026683617076,
          -55.47771589077422,
          -55.66216999199799,
          -55.851364138906796,
          -56.03585121878141,
          -56.214831744774074,
          -56.39995271236985,
          -56.58363705134989,
          -56.75950712573621,
          -56.93740769051402,
          -57.1168915145049,
          -57.289572253638504,
          -57.46225504210772,
          -57.636166015598185,
          -57.805786473358964,
          -57.9741856105167,
          -58.14490703259626,
          -58.313466825129346,
          -58.47824702472428,
          -58.64230433592689,
          -58.8079734251042,
          -58.97014353929205,
          -59.131911927271204,
          -59.296136920002354,
          -59.45520359036883,
          -59.60741516527753,
          -59.76135339865153,
          -59.912205614653175,
          -60.05150857415546,
          -60.18664716926364,
          -60.317502418270905,
          -60.43957092631385,
          -60.55499322597076,
          -60.667636157341946,
          -60.768427018784784,
          -60.86241918672804,
          -60.95030085618347,
          -61.024580932148645,
          -61.09090587621887,
          -61.14914079411982,
          -61.19924314482764,
          -61.243621863530386,
          -61.27924651122599,
          -61.308987736621866,
          -61.33646385694965,
          -61.356871064629736,
          -61.36829243965916,
          -61.37162056962145,
          -61.36834045637813,
          -61.358295497544134,
          -61.33973503069145,
          -61.31174474146187,
          -61.27589148248306,
          -61.23023836809319,
          -61.17731596195805,
          -61.113512138554405,
          -61.028649750219785,
          -60.93001045593834,
          -60.82384294482543,
          -60.69624251216949,
          -60.55972314880028,
          -60.433607471193234,
          -60.29474747995763,
          -60.14437680918496,
          -59.98755662017712,
          -59.81625232872422,
          -59.630092005090916,
          -59.4384879071594,
          -59.23985580283991,
          -59.03086544552774,
          -58.810565355578,
          -58.56645955067877,
          -58.31358558746552,
          -58.05126619125516,
          -57.77794229365562,
          -57.492628781303466,
          -57.196442861836466,
          -56.904475931304425,
          -56.60044398559001,
          -56.28964708300861,
          -55.97015556762816,
          -55.643628494242414,
          -55.31709111332235,
          -54.97954037887618,
          -54.64790045365633,
          -54.317651966708176,
          -53.982465937851956,
          -53.64334996358776,
          -53.312591895660155,
          -52.971111887687975,
          -52.6257337142858,
          -52.29357659127428,
          -51.95586437945262,
          -51.60919991098627,
          -51.26137741673533,
          -50.91082793198764,
          -50.55143459403899,
          -50.191092358689446,
          -49.828981026510405,
          -49.46307985264355,
          -49.100211002516204,
          -48.72549656212283,
          -48.344906692079725,
          -47.96754912365586,
          -47.582986526218306,
          -47.1931479496242,
          -46.805680961076334,
          -46.417212011564004,
          -46.02552259840897,
          -45.639080269092474,
          -45.24927459176417,
          -44.8657141286857,
          -44.48264988590599,
          -44.091341587388044,
          -43.70440152496862,
          -43.326371335081944,
          -42.93756005495286,
          -42.55803152824457,
          -42.1903664745427,
          -41.80740101201049,
          -41.438957033848,
          -41.07750854574851,
          -40.70295329029283,
          -40.33943578167989,
          -39.980772947505955,
          -39.608478599421666,
          -39.24615187109048,
          -38.901931747594546,
          -38.53476931078258,
          -38.16549338446798,
          -37.81401858826104,
          -37.44533559265203,
          -37.07068585727125,
          -36.71589596720581,
          -36.35336140466468,
          -35.983587424183376,
          -35.62689074078295,
          -35.26379595055595,
          -34.891830326257534,
          -34.537016008039586,
          -34.1874053880579,
          -33.83597714224507,
          -33.49500373020275,
          -33.158504284874226,
          -32.8288894003938,
          -32.493755184990235,
          -32.159574972343606,
          -31.818825301923898,
          -31.475467812069407,
          -31.136281289512674,
          -30.78935523168383,
          -30.431421999563444,
          -30.072031137636504,
          -29.71609282391668,
          -29.347830919658357,
          -28.98622890885428,
          -28.634312915719445,
          -28.276106222720692,
          -27.932279655314392,
          -27.59773395312081,
          -27.24587215336978,
          -26.881798072009286,
          -26.540917457373784,
          -26.197509286650266,
          -25.83553656836154,
          -25.478593377686654,
          -25.12989298445228,
          -24.774320695924626,
          -24.401670454355557,
          -24.037421652994762,
          -23.687067506611392,
          -23.32705878057707,
          -22.950423811741636,
          -22.59592183223668,
          -22.237037367621134,
          -21.847983918721674,
          -21.46939605343931,
          -21.112800781158175,
          -20.737673349532134,
          -20.358806694038343,
          -20.02009580585816,
          -19.68095609086906,
          -19.315993464740046,
          -18.96930321847797,
          -18.6307647327169,
          -18.268324190475546,
          -17.91788963138427,
          -17.57342500397895,
          -17.222244756522777,
          -16.879332363613543,
          -16.541466620741822,
          -16.202772464928938,
          -15.880068764244909,
          -15.557220259294553,
          -15.24072952564827,
          -14.94019159380588,
          -14.636066417794233,
          -14.338861264876103,
          -14.058549792275725,
          -13.787132756761189,
          -13.521315821055818,
          -13.27643510934198,
          -13.04636834840875,
          -12.823762818203749,
          -12.628358179469453,
          -12.449217283160127,
          -12.273583188616836,
          -12.123268061812093,
          -11.98703435908888,
          -11.859319390730313,
          -11.74861724994712,
          -11.6512153114971,
          -11.561833526473844,
          -11.484745698728178,
          -11.421838965178488,
          -11.369843955080263,
          -11.327488766542356,
          -11.296131900010426,
          -11.274797050244334,
          -11.261901596663778,
          -11.256313185591026,
          -11.259614281391523,
          -11.272134050044054,
          -11.29400034356385,
          -11.32230236191854,
          -11.357576702821278,
          -11.400628066401854,
          -11.450635413938164,
          -11.50520105835824,
          -11.563180837625433,
          -11.629685655187425,
          -11.698675124714063,
          -11.769936504488717,
          -11.848240358620831,
          -11.929867369897622,
          -12.010760050168534,
          -12.097512482866327,
          -12.183385608408717,
          -12.270780511880975,
          -12.36365572795244,
          -12.456489639953709,
          -12.549005368335774,
          -12.646141765232894,
          -12.743051089847395,
          -12.836905193032365,
          -12.9345487600994,
          -13.02984022921658,
          -13.12291907495958,
          -13.2174132710384,
          -13.310069692007449,
          -13.399205328955079,
          -13.48773882522301,
          -13.575833194274283,
          -13.665087379027295,
          -13.75291775229126,
          -13.842459027864933,
          -13.932315756903538,
          -14.02184667456172,
          -14.110717417770104,
          -14.202385755977145,
          -14.296337079503425,
          -14.392231580873847,
          -14.490265070609134,
          -14.592781481421335,
          -14.710021643707668,
          -14.820510826764014,
          -14.937318734613797,
          -15.059614394723365,
          -15.18468965697846,
          -15.317302524132579,
          -15.453820183251077,
          -15.593608196508068,
          -15.743427487693591,
          -15.897111059648413,
          -16.05149836661001,
          -16.21660840683516,
          -16.384021062618345,
          -16.54230076541489,
          -16.709550275147727,
          -16.877126464877946,
          -17.037462017848203,
          -17.20263057702021,
          -17.373701002666728,
          -17.532423389450074,
          -17.69101434767841,
          -17.853090007971023,
          -18.008745583263284,
          -18.16424551966732,
          -18.327362883142065,
          -18.48893391110862,
          -18.64435899971885,
          -18.80399840054474,
          -18.96525149129647,
          -19.12749442059322,
          -19.289228895757486,
          -19.45741279118992,
          -19.624518082031788,
          -19.789264290616078,
          -19.957217899632273,
          -20.12554320365396,
          -20.291535359651412,
          -20.45661741374188,
          -20.624900762742314,
          -20.792490384542983,
          -20.955721909462937,
          -21.120630439016022,
          -21.2870585386575,
          -21.444982130001627,
          -21.598863656561335,
          -21.750643479669705,
          -21.896438373808422,
          -22.03910849233606,
          -22.17636904208855,
          -22.30540175462884,
          -22.42542341135726,
          -22.539146956257788,
          -22.644016031622645,
          -22.740484152312717,
          -22.836514716343093,
          -22.92764295559613,
          -23.012012970289483,
          -23.095118556658033,
          -23.17077480859399,
          -23.240066409121205,
          -23.305515989393733,
          -23.361728466694164,
          -23.412337074856616,
          -23.46037371829752,
          -23.50306443829218,
          -23.543747054539534,
          -23.58499815473238,
          -23.62041704711707,
          -23.654493695511366,
          -23.689535348467874,
          -23.719767272254945,
          -23.750525646015646,
          -23.779927190012543,
          -23.805992317431624,
          -23.829555186808896,
          -23.853796381897105,
          -23.876081246940547,
          -23.89663360763789,
          -23.916418952165216,
          -23.933755094216373,
          -23.94812616839284,
          -23.960289014763017,
          -23.97027853066918,
          -23.979346440291494,
          -23.988601818959726,
          -23.99748673065064,
          -24.00746230432093,
          -24.01957645060076,
          -24.033380097808386,
          -24.048066397906844,
          -24.063321226370473,
          -24.08014814477246,
          -24.09751014798169,
          -24.115132668007714,
          -24.134855522500235,
          -24.157898249969136,
          -24.184071663509478,
          -24.21053352668448,
          -24.236998685094562,
          -24.26325365204827,
          -24.289106883822285,
          -24.316311335503762,
          -24.34603774911967,
          -24.37588825465715,
          -24.407686256573594,
          -24.441138420094155,
          -24.477407778640487,
          -24.515457326758536,
          -24.557349688165694,
          -24.601587495378162,
          -24.64748235127934,
          -24.69755047368866,
          -24.75077809488096,
          -24.80578761517861,
          -24.873895518769565,
          -24.94448774858941,
          -25.019008543138536,
          -25.09892525500434,
          -25.185604718885763,
          -25.27307780410482,
          -25.364576689331386,
          -25.46244295885574,
          -25.558943346151434,
          -25.65575028695536,
          -25.759876023316302,
          -25.864454463336454,
          -25.96961375458354,
          -26.079170181308427,
          -26.18634383147922,
          -26.29915145418115,
          -26.41859651341646,
          -26.536725175124598,
          -26.661264026478797,
          -26.793935149400237,
          -26.92695335525144,
          -27.06890445470459,
          -27.223066003407094,
          -27.387049201077836,
          -27.564426325664687,
          -27.747572176016874,
          -27.93471931049071,
          -28.13436605320347,
          -28.343737508465473,
          -28.56782487399333,
          -28.790516962230615,
          -29.014180773919982,
          -29.264963800505228,
          -29.514241258752172,
          -29.7507494894846,
          -29.999709328402282,
          -30.25566379689364,
          -30.509285098859056,
          -30.767976423346198,
          -31.030391781940747,
          -31.292404341267684,
          -31.555709870094105,
          -31.812829165823533,
          -32.06157084192572,
          -32.31126090315761,
          -32.55430156850084,
          -32.7874250918752,
          -33.013204134689765,
          -33.228245201726686,
          -33.45056213359985,
          -33.64115367671727,
          -33.823531279904536,
          -33.994139037296264,
          -34.15613190979066,
          -34.31141144239608,
          -34.456150439498195,
          -34.59114376810545,
          -34.71902504617575,
          -34.83792158668946,
          -34.94790477840534,
          -35.050416574223746,
          -35.14510074675099,
          -35.23517737454116,
          -35.32256305773505,
          -35.40517143426763,
          -35.48535672371655,
          -35.57405311539677,
          -35.65501447059158,
          -35.738099251115855,
          -35.822642876840526,
          -35.90917545965357,
          -36.00047594326388,
          -36.09321222872469,
          -36.18752861473809,
          -36.284240303576944,
          -36.3836798712461,
          -36.48809319057018,
          -36.59313018240287,
          -36.700604561550676,
          -36.81453474991191,
          -36.93311730567894,
          -37.05309845188107,
          -37.17928359079711,
          -37.31323857749552,
          -37.44761451769284,
          -37.588284057073025,
          -37.73227708031916,
          -37.88325501482355,
          -38.04140478248731,
          -38.20044180813364,
          -38.37094435449853,
          -38.55112897531844,
          -38.72710070636912,
          -38.90885426980683,
          -39.104773756264535,
          -39.301469076443794,
          -39.50092913661933,
          -39.71551269943364,
          -39.93246932757636,
          -40.14419470742514,
          -40.36403088471037,
          -40.61237982379394,
          -40.837449775604206,
          -41.064227857947046,
          -41.296263191665865,
          -41.53250161080576,
          -41.77005786741688,
          -42.00642155578498,
          -42.245692909403644,
          -42.48615083355477,
          -42.72627120320868,
          -42.967784276973255,
          -43.210838389998216,
          -43.454905027997754,
          -43.69656572062917,
          -43.939071522217255,
          -44.17748578944402,
          -44.40877356683387,
          -44.63746220975535,
          -44.86686969668305,
          -45.087741067713004,
          -45.30470116652954,
          -45.526841861896855,
          -45.74381477345993,
          -45.9582240033877,
          -46.17520740545471,
          -46.38988522520938,
          -46.60260269830783,
          -46.815076231505415,
          -47.0306596826408,
          -47.246494086527896,
          -47.45431443616966,
          -47.66179794852654,
          -47.869890858231095,
          -48.07051691276318,
          -48.26658740305062,
          -48.45822715782399,
          -48.637913969054864,
          -48.81847286901816,
          -48.9981089964212,
          -49.168131845598005,
          -49.33503788461863,
          -49.502372581737816,
          -49.664890882012045,
          -49.82532662495358,
          -49.985368463902745,
          -50.141289377818886,
          -50.29445671935501,
          -50.44537527216848,
          -50.595209995241746,
          -50.73987131413586,
          -50.880321205825396,
          -51.02053233594645,
          -51.15862052568441,
          -51.29209638461525,
          -51.423227850287695,
          -51.554193325480924,
          -51.682263827662155,
          -51.80818966783331,
          -51.933267353127604,
          -52.05329760709906,
          -52.16949175990998,
          -52.28678490748444,
          -52.39775833318429,
          -52.50647880540683,
          -52.61359443602876,
          -52.71846518731468,
          -52.82032291602857,
          -52.92044824595632,
          -53.017292305290745,
          -53.113265566743245,
          -53.20682483440556,
          -53.29549837615724,
          -53.38050501526027,
          -53.463008615655816,
          -53.54278518028811,
          -53.620062293650314,
          -53.69609395213598,
          -53.77152277654935,
          -53.84653840152321,
          -53.92166157519881,
          -53.996279591142375,
          -54.06956555485206,
          -54.13976662425757,
          -54.21010790595168,
          -54.281335950198425,
          -54.34868707516771,
          -54.41624017478141,
          -54.48455688045824,
          -54.551068776349425,
          -54.61574435450012,
          -54.6819684659621,
          -54.74687315211124,
          -54.80981745893463,
          -54.87483829002289,
          -54.9400734205884,
          -55.00410148869024,
          -55.069917202635196,
          -55.136939217187624,
          -55.201861944524815,
          -55.266327934074646,
          -55.3317541238993,
          -55.39720755610121,
          -55.463251249573375,
          -55.53183612633831,
          -55.600815659007544,
          -55.66866888302588,
          -55.73855766178132,
          -55.81094806659809,
          -55.88274360338026,
          -55.954410878287604,
          -56.02335995616113,
          -56.08653911246893,
          -56.14528801778404,
          -56.19830731489368,
          -56.24522663731658,
          -56.28597955798271,
          -56.32190276823193,
          -56.3519461383363,
          -56.37527715778535,
          -56.396000943071016,
          -56.410295107175,
          -56.41748415160509,
          -56.41511941982913,
          -56.40461982918199,
          -56.383780435378,
          -56.35053751793998,
          -56.308371808596924,
          -56.25699922373871,
          -56.190261226826806,
          -56.11489109327586,
          -56.028361132762754,
          -55.93528832066313,
          -55.841011086953536,
          -55.73248273941255,
          -55.60947684380252,
          -55.485133563840606,
          -55.34974633710588,
          -55.199200316763275,
          -55.0485683988637,
          -54.88546118863054,
          -54.71185208986849,
          -54.53821924360358,
          -54.33865137751723,
          -54.12676993446414,
          -53.917672564784866,
          -53.687481928798,
          -53.45247952617786,
          -53.224167600110626,
          -52.979675778149875,
          -52.722402522782346,
          -52.46592382551485,
          -52.197801370097416,
          -51.92043424125247,
          -51.6485256498487,
          -51.367855919960384,
          -51.07225456512394,
          -50.77220138000718,
          -50.46125676473004,
          -50.13988620861913,
          -49.81387251704995,
          -49.4738458398497,
          -49.12946373042813,
          -48.785439747863265,
          -48.43348449840709,
          -48.07354271016477,
          -47.71001644719917,
          -47.340243406625554,
          -46.975552243235605,
          -46.606976228357844,
          -46.22669179650427,
          -45.86232697645387,
          -45.50328789610202,
          -45.12665413967861,
          -44.755393662619745,
          -44.398697318781515,
          -44.0201703619642,
          -43.637921578937195,
          -43.26707798347966,
          -42.88661844403491,
          -42.49221634638106,
          -42.10257554309159,
          -41.70620510737677,
          -41.30404826516985,
          -40.9024725592768,
          -40.49695324808783,
          -40.094203832165476,
          -39.69326197760276,
          -39.28467981906957,
          -38.87706873985989,
          -38.466767667351284,
          -38.05063278221215,
          -37.63793009967038,
          -37.22773802824038,
          -36.81081745582405,
          -36.39950435349942,
          -35.98740807079116,
          -35.564018296971405,
          -35.148622793218735,
          -34.72901355973301,
          -34.298855382619536,
          -33.881001233161356,
          -33.4693413907427,
          -33.04501771609204,
          -32.63845031857292,
          -32.232698830429094,
          -31.82058640190152,
          -31.416293177928125,
          -31.005664782491984,
          -30.59279361029727,
          -30.187209070318314,
          -29.7785167447167,
          -29.36659548355264,
          -28.975365030880102,
          -28.57445136808079,
          -28.163977619406293,
          -27.767587830956874,
          -27.373414255606882,
          -26.968516842274514,
          -26.576998991782002,
          -26.187220189614244,
          -25.788177672808217,
          -25.396856976222026,
          -25.001445620704846,
          -24.603457091701628,
          -24.219371761407537,
          -23.841161581728375,
          -23.470260057496493,
          -23.108014999801455,
          -22.750004117400216,
          -22.395414135020793,
          -22.042610659048606,
          -21.681270616376256,
          -21.27553134551176,
          -20.913105879888324,
          -20.545781587335025,
          -20.165478262334542,
          -19.78378104021787,
          -19.400186955075686,
          -19.016874466607028,
          -18.63313242754503,
          -18.254355086592316,
          -17.896259493530156,
          -17.552332572435873,
          -17.213033571797308,
          -16.875962974781757,
          -16.541937239717203,
          -16.206102587589175,
          -15.87676286308467,
          -15.511972688126127,
          -15.17600829607498,
          -14.83721674879326,
          -14.490093131839615,
          -14.12861908582576,
          -13.757097672089284,
          -13.401345155840602,
          -13.04533635724029,
          -12.670252886350644,
          -12.302212745396481,
          -11.953371368277988,
          -11.585828201277513,
          -11.214590856602351,
          -10.88435258245321,
          -10.559012936539022,
          -10.228991082741462,
          -9.91140558037379,
          -9.602436805693412,
          -9.300126927048481,
          -8.986836483092265,
          -8.678457907452758,
          -8.379091726896203,
          -8.069251023296742,
          -7.754712908155948,
          -7.448270919620779,
          -7.147601267393443,
          -6.8583619753513405,
          -6.5769804042732485,
          -6.307367057079339,
          -6.05631914282536,
          -5.813724319815339,
          -5.5814076355931626,
          -5.368911812062815,
          -5.192783199868777,
          -5.026022995334309,
          -4.868573670790678,
          -4.724075731613454,
          -4.592754795067297,
          -4.4657171934561175,
          -4.355142645668079,
          -4.2596546851801955,
          -4.173412975318418,
          -4.0955037984464555,
          -4.024808370968408,
          -3.968051835537542,
          -3.9241973889923254,
          -3.891067199301055,
          -3.869707371482235,
          -3.860122070435745,
          -3.862495398975393,
          -3.8775151213606383,
          -3.9073570620714304,
          -3.950451835597978,
          -4.005461239337054,
          -4.071208160032066,
          -4.143380125248869,
          -4.2255319121017045,
          -4.3171473076338565,
          -4.413934691448962,
          -4.521982882453739,
          -4.639687833005884,
          -4.760098636788015,
          -4.887110188807535,
          -5.0261006886480075,
          -5.1661996110564985,
          -5.309491523231896,
          -5.468176571958472,
          -5.622253537883207,
          -5.777285976835671,
          -5.946373579698685,
          -6.111283969646562,
          -6.2717260228459395,
          -6.444205063808137,
          -6.609813145526646,
          -6.773720264899113,
          -6.946045975631996,
          -7.118808272128241,
          -7.291485921054185,
          -7.470831606503378,
          -7.6533696746314686,
          -7.830199685370139,
          -8.013377255497419,
          -8.199564393590066,
          -8.384530603791417,
          -8.57276708100062,
          -8.764092264635837,
          -8.952026334503474,
          -9.13889061141238,
          -9.32698380261516,
          -9.513847103890624,
          -9.706681451985856,
          -9.894284923289993,
          -10.085215369996689,
          -10.27397743810571,
          -10.46183393625287,
          -10.647675203668975,
          -10.83098793418853,
          -11.0184310312165,
          -11.205597764385988,
          -11.392168810711311,
          -11.58054114554603,
          -11.770043530402754,
          -11.961243643568931,
          -12.1545095518784,
          -12.355773155038113,
          -12.561455602769636,
          -12.765464418300763,
          -12.978933786165262,
          -13.194811307411582,
          -13.407949114803971,
          -13.630138801875,
          -13.857851236022755,
          -14.085204476989372,
          -14.321819793004368,
          -14.575182510486046,
          -14.817720769469934,
          -15.059573005267572,
          -15.319242183165702,
          -15.568876804424663,
          -15.818823975065168,
          -16.08258642563926,
          -16.34223874940074,
          -16.594629894743363,
          -16.849567870978728,
          -17.10579657033175,
          -17.353681398093396,
          -17.60653299805298,
          -17.85999035414474,
          -18.115673612600467,
          -18.364967465806743,
          -18.614438650252584,
          -18.86587359078524,
          -19.12120535304735,
          -19.374476650515412,
          -19.63153293056934,
          -19.89687143489585,
          -20.15350283626709,
          -20.408118024224827,
          -20.6622972824969,
          -20.9206815476821,
          -21.170248923250337,
          -21.419776681362926,
          -21.67249004929207,
          -21.919020154425592,
          -22.1637044896756,
          -22.410109019447614,
          -22.657707212892188,
          -22.900690166227275,
          -23.144291468724422,
          -23.386332664981293,
          -23.619115263115102,
          -23.857131862490455,
          -24.09024445190506,
          -24.30498132329061,
          -24.517780954673,
          -24.7221849723308,
          -24.921015255880473,
          -25.114219513598446,
          -25.302940490263403,
          -25.488321719857403,
          -25.672226604487538,
          -25.85034856713363,
          -26.025582336955623,
          -26.197591896228154,
          -26.367651795131177,
          -26.533327549794155,
          -26.687755042423557,
          -26.84055578832506,
          -26.99019647315873,
          -27.13144868285428,
          -27.27161008377521,
          -27.41667790440846,
          -27.55109559756212,
          -27.68300506668926,
          -27.82638961081035,
          -27.961846992981275,
          -28.091233357668013,
          -28.230263054923775,
          -28.36639169618012,
          -28.499690495293102,
          -28.639337022166554,
          -28.78225615330068,
          -28.925094595024095,
          -29.074026903283965,
          -29.22403424232948,
          -29.36953502485965,
          -29.514981072534624,
          -29.65695376722536,
          -29.79644485744043,
          -29.933882283035597,
          -30.071653917496093,
          -30.20816723332997,
          -30.343842071599965,
          -30.479793962838674,
          -30.613787436791135,
          -30.748708557112543,
          -30.881033307151984,
          -31.0138450544275,
          -31.146690908358817,
          -31.279007427202927,
          -31.41167946785834,
          -31.546737361526997,
          -31.68530424271964,
          -31.824093766050275,
          -31.960275171462246,
          -32.09844380117443,
          -32.23595195995335,
          -32.3676118801337,
          -32.49858677699923,
          -32.63402351098039,
          -32.759013349903206,
          -32.88413080127819,
          -33.010907599257344,
          -33.133380285877834,
          -33.252723920535594,
          -33.36996619896849,
          -33.48668704809511,
          -33.603491435704406,
          -33.716355338377284,
          -33.8314707763821,
          -33.953498808178054,
          -34.07512651098753,
          -34.19538041646202,
          -34.32816727584279,
          -34.46144232930978,
          -34.59423893382527,
          -34.742769721067916,
          -34.895522536009594,
          -35.044393623940934,
          -35.2073585096373,
          -35.37265462129525,
          -35.53867091655266,
          -35.71943923683007,
          -35.88801817525376,
          -36.06067544629365,
          -36.247107654796665,
          -36.42679064269483,
          -36.60985158483766,
          -36.80783599136066,
          -37.00587038488824,
          -37.208502067013846,
          -37.422226501665655,
          -37.639281013634104,
          -37.86121207151336,
          -38.09646877474403,
          -38.34092748182813,
          -38.590685452105404,
          -38.848909520509714,
          -39.11534274278885,
          -39.39261077527654,
          -39.67639588567982,
          -39.96087646625901,
          -40.25329494474936,
          -40.54763068668886,
          -40.83297928839565,
          -41.129295480945906,
          -41.421726408290645,
          -41.70723149140203,
          -41.990465458619425,
          -42.2651421955693,
          -42.530352843379895,
          -42.786404516998175,
          -43.03274648205944,
          -43.26590034036846,
          -43.481356339301776,
          -43.686525766160955,
          -43.8759252958635,
          -44.04559167635969,
          -44.19806839619527,
          -44.33188127186157,
          -44.44866487897621,
          -44.551215280360594,
          -44.63752047436132,
          -44.707535091993755,
          -44.76388811729896,
          -44.81173765941115,
          -44.843079376071046,
          -44.86580402296306,
          -44.881708484165394,
          -44.890293460786985,
          -44.892259994242096,
          -44.888906890095846,
          -44.87985243749461,
          -44.86664418299311,
          -44.850639535998425,
          -44.832439078434206,
          -44.81307697045818,
          -44.79364821576541,
          -44.77503496468325,
          -44.75793184471923,
          -44.74349179460754,
          -44.73134203405788,
          -44.72030702815232,
          -44.69249268903152,
          -44.6996869826273,
          -44.71391958127997,
          -44.735883976569475,
          -44.765254335205896,
          -44.80170001153461,
          -44.84530831853433,
          -44.895772991062024,
          -44.95219263712336,
          -45.01473332775103,
          -45.08399352928447,
          -45.15996747740505,
          -45.24347836402794,
          -45.33845839365368,
          -45.43750344941558,
          -45.536366746199725,
          -45.643487327307824,
          -45.75842306715362,
          -45.87238738167741,
          -45.994168329078256,
          -46.12390089910052,
          -46.25115217236301,
          -46.38101718408689,
          -46.517506831728014,
          -46.6550714716193,
          -46.794282173775485,
          -46.93871939461475,
          -47.08870503777707,
          -47.24106231918847,
          -47.39492903767727,
          -47.552106407831616,
          -47.71069482163378,
          -47.86833471880161,
          -48.02825171483278,
          -48.19088735949445,
          -48.35367350272166,
          -48.5164819191643,
          -48.681022375298,
          -48.84166040674982,
          -48.998435418748194,
          -49.15419224791821,
          -49.30854843717438,
          -49.45737026800353,
          -49.60656826089752,
          -49.75758195482167,
          -49.902628690297306,
          -50.04873698515476,
          -50.19615653120516,
          -50.33994110158995,
          -50.480549863079794,
          -50.622008878640365,
          -50.76133541333833,
          -50.8929643832669,
          -51.02233515820244,
          -51.14895945137354,
          -51.2680988597582,
          -51.38051322461153,
          -51.484596065755014,
          -51.57966171816269,
          -51.67284228761277,
          -51.759502972305945,
          -51.83940366411082,
          -51.91587332061889,
          -51.98798567467568,
          -52.055661050170094,
          -52.119569779834634,
          -52.179991988245625,
          -52.236473421664535,
          -52.290181235386555,
          -52.33967545133591,
          -52.38385351938186,
          -52.42412489048871,
          -52.46170592983039,
          -52.496379272571275,
          -52.52794835091763,
          -52.55640817046599,
          -52.58053487776926,
          -52.600000458811806,
          -52.613722002239975,
          -52.62350810992837,
          -52.62996018638715,
          -52.63343479455111,
          -52.633980907247164,
          -52.630943992008476,
          -52.62467450630691,
          -52.61612382426644,
          -52.60476322398838,
          -52.59057986977051,
          -52.574046200361074,
          -52.555570291267216,
          -52.535628720336824,
          -52.51400646619419,
          -52.48791643702848,
          -52.45849939065624,
          -52.426490217563206,
          -52.39189322700984,
          -52.35474224440913,
          -52.31584925846777,
          -52.27685866076428,
          -52.23899018369706,
          -52.20150409459526,
          -52.162776399484635,
          -52.12304343355836,
          -52.08512991409284,
          -52.0461224656918,
          -52.00514312276096,
          -51.96440843197896,
          -51.92084551384291,
          -51.87287870672525,
          -51.82307010778093,
          -51.772298034008365,
          -51.72023068227053,
          -51.667030281223816,
          -51.61417873608414,
          -51.56225592335788,
          -51.509952259223745,
          -51.458071560477855,
          -51.408907919267264,
          -51.36289940655628,
          -51.318446525474,
          -51.27513817666198,
          -51.23343081073004,
          -51.192150494659984,
          -51.14880593328901,
          -51.10552068083719,
          -51.06348656722617,
          -51.022793497279615,
          -50.98218273023084,
          -50.942458104881574,
          -50.90333209393517,
          -50.86399556579007,
          -50.82371783660683,
          -50.78285149382917,
          -50.74063371446675,
          -50.69590802453579,
          -50.64616604322733,
          -50.59426317388249,
          -50.54021665142166,
          -50.48125913923025,
          -50.4159489221181,
          -50.34573461699959,
          -50.27601953353696,
          -50.19607363984064,
          -50.1091936597282,
          -50.020274412215954,
          -49.92751626418495,
          -49.83029165712424,
          -49.72593195712166,
          -49.613775234690515,
          -49.50052865968491,
          -49.379349222896074,
          -49.25032717896444,
          -49.119444992439774,
          -48.98069563185496,
          -48.829240981162926,
          -48.68317797721376,
          -48.524230507127044,
          -48.357094358307926,
          -48.18913215749813,
          -48.00296609363351,
          -47.813956589409116,
          -47.62526973423658,
          -47.4202582006301,
          -47.211026671998845,
          -47.00100327179271,
          -46.77265217918488,
          -46.54583321854025,
          -46.31148139389012,
          -46.048383374484736,
          -45.786075026934384,
          -45.51444151562943,
          -45.22318886053367,
          -44.94310777165705,
          -44.66655916779887,
          -44.37079048660445,
          -44.07328916933107,
          -43.77760952714714,
          -43.46228592311404,
          -43.14300318049824,
          -42.8299257989286,
          -42.50778530170045,
          -42.18033867939624,
          -41.84944077635536,
          -41.51096936196984,
          -41.171839551467016,
          -40.82660420735386,
          -40.472401955940995,
          -40.11561997539666,
          -39.764207205288514,
          -39.40585787372262,
          -39.041387040642384,
          -38.675513535158515,
          -38.31160371356203,
          -37.95185106102344,
          -37.583940709792145,
          -37.21400006015976,
          -36.862613482193815,
          -36.51330918301553,
          -36.15141824953603,
          -35.800358567377984,
          -35.459571629845264,
          -35.09943945327148,
          -34.74059028489571,
          -34.39428050806257,
          -34.036348280582615,
          -33.66769338599005,
          -33.3061227815726,
          -32.93681771785011,
          -32.558864420188826,
          -32.184908142543804,
          -31.80646051263562,
          -31.428248350729074,
          -31.057021006462573,
          -30.680559309450924,
          -30.29930409057992,
          -29.924490614829747,
          -29.54454141384704,
          -29.162933575628614,
          -28.784312689581878,
          -28.408811023483157,
          -28.02957905323498,
          -27.65748997836576,
          -27.278908053004926,
          -26.900956821644524,
          -26.527388781437157,
          -26.14438945089141,
          -25.763103298989105,
          -25.390813823245367,
          -25.015638730734423,
          -24.635898301341562,
          -24.277690192581534,
          -23.909719258693144,
          -23.540331987477405,
          -23.186638603304758,
          -22.82197620132539,
          -22.45300542515495,
          -22.097185015213235,
          -21.737532249434736,
          -21.371056921395777,
          -21.012577134921433,
          -20.666636844946296,
          -20.307038412830885,
          -19.948720373033876,
          -19.597577281640667,
          -19.246936206017725,
          -18.89159592676133,
          -18.545277410556288,
          -18.20121162170815,
          -17.851966325494715,
          -17.508052562998092,
          -17.167770769304795,
          -16.821076220366233,
          -16.47946607988687,
          -16.145744793266836,
          -15.814228922530297,
          -15.491805258234203,
          -15.179677523464361,
          -14.8633627512647,
          -14.557037617349037,
          -14.253843341729306,
          -13.944987813427646,
          -13.635629095741681,
          -13.322281360388635,
          -13.012004316164749,
          -12.698719522178457,
          -12.375354008410984,
          -12.046641556605602,
          -11.712787415317722,
          -11.376614517001714,
          -11.040394907385506,
          -10.702720618533457,
          -10.362559867057287,
          -10.03061645103251,
          -9.707980959615293,
          -9.38440903905259,
          -9.059834976066892,
          -8.734203012823148,
          -8.41805821291957,
          -8.100012267881002,
          -7.773826376060623,
          -7.447778200975354,
          -7.1184738164268335,
          -6.795318826940068,
          -6.456722035195495,
          -6.117266938576435,
          -5.7866646071535675,
          -5.452889040131884,
          -5.101611510399121,
          -4.764240990674404,
          -4.436876820100168,
          -4.087136277317069,
          -3.7418598571742168,
          -3.4241903364665935,
          -3.103473435967006,
          -2.7788705640082556,
          -2.485939087116193,
          -2.2092911445964023,
          -1.9102302910029092,
          -1.6173485489608996,
          -1.346405576436552,
          -1.0670108169783246,
          -0.7977185809825318,
          -0.5484779523677786,
          -0.29859945955637024,
          -0.061841161178086995,
          0.16448661684993626,
          0.3841144497276622,
          0.5867262104084506,
          0.7707135775219899,
          0.9446706703707425,
          1.1018653867297192,
          1.2443708560725106,
          1.3837252634150707,
          1.5096321328587712,
          1.6158006419000692,
          1.707777574760611,
          1.7869280304255042,
          1.8499632932751935,
          1.8943460035923738,
          1.9212024056325951,
          1.9282960145211037,
          1.917817362532113,
          1.8864847970915535,
          1.8374243200313785,
          1.7741355270940877,
          1.6897934949524558,
          1.5912510242380387,
          1.4802031868357792,
          1.3515261774411509,
          1.203421348234305,
          1.0448401000523437,
          0.873293391818103,
          0.6845743378337061,
          0.48831273855358437,
          0.28777000970844396,
          0.07933697037023946,
          -0.13688849636368336,
          -0.35883808203806244,
          -0.5824375509874291,
          -0.8098234100091103,
          -1.043231861384742,
          -1.2817768081554781,
          -1.520391387343699,
          -1.76571433172012,
          -2.017623614445508,
          -2.267746428346875,
          -2.5171593167391517,
          -2.780965140001806,
          -3.0374773839757703,
          -3.2879731480628536,
          -3.5511411050417214,
          -3.812005961062005,
          -4.062173802661583,
          -4.3241936020579885,
          -4.584631865759376,
          -4.838889944192866,
          -5.103219898911103,
          -5.3860529376514785,
          -5.67653719234623,
          -5.975693892712216,
          -6.279804512355977,
          -6.576325874713259,
          -6.8789860937068905,
          -7.188447734974245,
          -7.492947550366757,
          -7.799447499143733,
          -8.111691199367367,
          -8.40422873334024,
          -8.68505581379873,
          -8.96735922985983,
          -9.247395022849393,
          -9.532148029176163,
          -9.811745409174838,
          -10.09695940223443,
          -10.382500903677133,
          -10.665319975781946,
          -10.946664751406837,
          -11.237903100529563,
          -11.541335122632427,
          -11.844730606419335,
          -12.147499968901313,
          -12.458264678458884,
          -12.768826734965083,
          -13.082203961327481,
          -13.395786454899332,
          -13.719506417967747,
          -14.043151773165096,
          -14.351713746912496,
          -14.660910477428597,
          -14.965990758885457,
          -15.27002094724147,
          -15.585344209431796,
          -15.898666411115586,
          -16.209075784159566,
          -16.533446215676193,
          -16.864127276059868,
          -17.174480366931117,
          -17.4684255916292,
          -17.75305947463326,
          -18.018662261851215,
          -18.28817989298486,
          -18.570346264010272,
          -18.837537510652222,
          -19.097866518194827,
          -19.371515472780914,
          -19.63946804818005,
          -19.901653887969136,
          -20.192591710752406,
          -20.496584416781534,
          -20.80453937159835,
          -21.106293859934464,
          -21.40740926541604,
          -21.71235840809054,
          -22.022894799656644,
          -22.325192821906608,
          -22.625615940203158,
          -22.94236583559797,
          -23.24129787830059,
          -23.5297764922627,
          -23.820261712351282,
          -24.114438784228476,
          -24.40505482803702,
          -24.69024388532251,
          -24.980994512419564,
          -25.2662303956687,
          -25.55521384575851,
          -25.842454884994655,
          -26.13866400472831,
          -26.436809303890584,
          -26.728314163166203,
          -27.024496327804812,
          -27.313159457627815,
          -27.595955846558883,
          -27.88173449603556,
          -28.15927234762725,
          -28.432499269756363,
          -28.706573461440055,
          -28.97165345463406,
          -29.24091483378553,
          -29.513117955874556,
          -29.777739955927895,
          -30.045782300939948,
          -30.31930157945917,
          -30.586529277498784,
          -30.85294189001411,
          -31.124288832352487,
          -31.388692671859268,
          -31.64526886462561,
          -31.91066119942439,
          -32.164018041278524,
          -32.412152720246944,
          -32.66492625526931,
          -32.92390382094429,
          -33.16281383558861,
          -33.4031736766098,
          -33.6620600313757,
          -33.90006089539899,
          -34.143799184675665,
          -34.400591909596464,
          -34.64662141364417,
          -34.889028061874605,
          -35.13660210260092,
          -35.385863748383926,
          -35.62891602906219,
          -35.876861842075805,
          -36.12230259571905,
          -36.36165468512135,
          -36.597918705609075,
          -36.8305393027967,
          -37.061513262028065,
          -37.29367944609783,
          -37.53013267649586,
          -37.761760565043296,
          -37.99867332980302,
          -38.23503373913347,
          -38.47257909285061,
          -38.71522076192912,
          -38.95468842645664,
          -39.19600129828062,
          -39.44281759022477,
          -39.689096679733495,
          -39.935277150649554,
          -40.185340621989184,
          -40.44270012327779,
          -40.69700686925106,
          -40.947604704997126,
          -41.20357316572996,
          -41.45874687175612,
          -41.705575390757986,
          -41.950407032641735,
          -42.2057428328899,
          -42.44484924723598,
          -42.68167380825259,
          -42.924384541809914,
          -43.15453416835302,
          -43.38447302893445,
          -43.618030375520874,
          -43.85006631917921,
          -44.082708269384824,
          -44.31670989633449,
          -44.547957923265855,
          -44.78630139238495,
          -45.02791171860808,
          -45.26382763836701,
          -45.512312043293115,
          -45.7543493885623,
          -45.99292295377146,
          -46.240180231005276,
          -46.48476619484078,
          -46.72583368767717,
          -46.97000561210904,
          -47.215377647267445,
          -47.45722013201295,
          -47.70323221192097,
          -47.941871473538235,
          -48.17756106845346,
          -48.41923672459774,
          -48.65393415152999,
          -48.88709752111466,
          -49.12767628102655,
          -49.369436237810774,
          -49.61340333337116,
          -49.860886129774926,
          -50.11424063264458,
          -50.373259092667546,
          -50.639647444283,
          -50.911504562297914,
          -51.18945881614874,
          -51.47353348374666,
          -51.75583442446818,
          -52.0468763170805,
          -52.344808366209335,
          -52.6320520795149,
          -52.90692873021462,
          -53.19002579230331,
          -53.469100992392214,
          -53.730143535404515,
          -53.98894162744045,
          -54.23764698050932,
          -54.469555428785576,
          -54.688008998443244,
          -54.89019073834005,
          -55.07186501266503,
          -55.23165307667545,
          -55.3732870634124,
          -55.49378057002766,
          -55.590710360531396,
          -55.66532866871269,
          -55.717525811303936,
          -55.75066885955313,
          -55.76481512072593,
          -55.759891092974605,
          -55.73724106254656,
          -55.69729589255787,
          -55.64060541527604,
          -55.56834567111792,
          -55.48177187454085,
          -55.383542300915664,
          -55.27491394895366,
          -55.15645320520226,
          -55.03284645498123,
          -54.90260828196945,
          -54.767051200225715,
          -54.629698754699795,
          -54.48874693444187,
          -54.346638011117626,
          -54.20731475330449,
          -54.07363022510151,
          -53.93196722252462,
          -53.80831329558492,
          -53.69114650339178,
          -53.57786601284826,
          -53.469043869138225,
          -53.3657755501066,
          -53.2670069393885,
          -53.17308914387623,
          -53.08615017251135,
          -53.00551961166567,
          -52.93392858581801,
          -52.87073627139909,
          -52.812357963286885,
          -52.76213472629049,
          -52.717720751099606,
          -52.67911497873581,
          -52.64225787403717,
          -52.61330178705449,
          -52.594676919791304,
          -52.58082521513664,
          -52.571383870721235,
          -52.56542523904344,
          -52.5630785770816,
          -52.565592370876516,
          -52.57291237735343,
          -52.58616924586441,
          -52.603678154010616,
          -52.62296230917877,
          -52.644724206431114,
          -52.67165037532843,
          -52.702284323820884,
          -52.737154780288485,
          -52.77689231566481,
          -52.82004447580215,
          -52.86531443987108,
          -52.91387719640536,
          -52.96428709593051,
          -53.01436406118113,
          -53.06484444653372,
          -53.117922809677495,
          -53.171181093997106,
          -53.22458916017944,
          -53.279133522095115,
          -53.33052337704517,
          -53.378733418019564,
          -53.42607164702704,
          -53.4714046698874,
          -53.51481297136362,
          -53.557944350815504,
          -53.598259257367445,
          -53.636102223438186,
          -53.67274066725741,
          -53.70648333263322,
          -53.7354858649595,
          -53.761058642241586,
          -53.78300186441062,
          -53.79922034263283,
          -53.809134573170724,
          -53.81419992696705,
          -53.812247757428295,
          -53.80373956340987,
          -53.78878642993154,
          -53.769409349898694,
          -53.74473539493373,
          -53.71516183313104,
          -53.678488530788805,
          -53.63643698267936,
          -53.590771397281955,
          -53.538796494073715,
          -53.47975676217477,
          -53.41637368491696,
          -53.3497085120415,
          -53.27559987391911,
          -53.19991727447366,
          -53.1208453439042,
          -53.03571923129624,
          -52.949456604697666,
          -52.86298781084249,
          -52.770943878812425,
          -52.67350404144981,
          -52.577987350008115,
          -52.47545301673853,
          -52.36682885794369,
          -52.25597378162846,
          -52.14208990752695,
          -52.024303232727576,
          -51.90702509388509,
          -51.787273710472974,
          -51.66571118214049,
          -51.54266789484829,
          -51.41738781292871,
          -51.28946596887473,
          -51.16052080253384,
          -51.02866508449045,
          -50.8967711691289,
          -50.76261493370004,
          -50.624378145049164,
          -50.484817041196,
          -50.34337387757248,
          -50.20008854303476,
          -50.0538283194695,
          -49.906382587265696,
          -49.76005205696314,
          -49.61522890373951,
          -49.46798359797079,
          -49.32205414306024,
          -49.18168893804091,
          -49.03706712113395,
          -48.88939627432503,
          -48.73172291378426,
          -48.5841774399688,
          -48.43013737911197,
          -48.276852452440046,
          -48.124153931719825,
          -47.966186745995046,
          -47.80676532177742,
          -47.65060753173576,
          -47.49206214765714,
          -47.32980473958183,
          -47.17081699044504,
          -47.013375283800286,
          -46.85609451728255,
          -46.69841323654441,
          -46.54233532256226,
          -46.38772590626042,
          -46.23045540429578,
          -46.072997353744526,
          -45.91985572568633,
          -45.767809867773444,
          -45.59778214886511,
          -45.4471504016637,
          -45.29859410580334,
          -45.14745006215438,
          -44.994958896543324,
          -44.84172223777462,
          -44.685277819059,
          -44.5221124740435,
          -44.35867921694125,
          -44.195839378625294,
          -44.03100821053184,
          -43.85770043495074,
          -43.6831017161419,
          -43.51147692747272,
          -43.324363683492656,
          -43.1341969492792,
          -42.943091506016266,
          -42.7474159172583,
          -42.547946375969765,
          -42.343132635624364,
          -42.120768303065276,
          -41.897350622455434,
          -41.66325160495242,
          -41.426558639232404,
          -41.18934403635728,
          -40.93616529212884,
          -40.6957372459493,
          -40.44246504964155,
          -40.18163899920708,
          -39.92434735393384,
          -39.668231026113034,
          -39.41623766824345,
          -39.1671557592698,
          -38.90258881561719,
          -38.639796655670395,
          -38.37732500748666,
          -38.0969814389229,
          -37.825939649866726,
          -37.54664444117788,
          -37.24150585378087,
          -36.945436630283055,
          -36.63431425760449,
          -36.31069019186036,
          -36.00875720739604,
          -35.70803315122114,
          -35.388528637443244,
          -35.07167294493991,
          -34.763215751620464,
          -34.43838892399438,
          -34.11452048772369,
          -33.78971758156607,
          -33.46110006712418,
          -33.132339748723815,
          -32.80562116904536,
          -32.47674906483984,
          -32.15090406653988,
          -31.82626137880774,
          -31.492741870296136,
          -31.161963129353094,
          -30.839768089453276,
          -30.493129347388155,
          -30.146136230801716,
          -29.807844869758554,
          -29.4740387069343,
          -29.150738082622137,
          -28.82972569412432,
          -28.497130844013107,
          -28.177648099772572,
          -27.86433405088853,
          -27.54673240484818,
          -27.23888274655231,
          -26.936622708354275,
          -26.63489587492054,
          -26.32161000472169,
          -26.012277100129033,
          -25.704170704376644,
          -25.387665290561017,
          -25.06487794695087,
          -24.742397351130883,
          -24.41396499075897,
          -24.081677491641894,
          -23.749454082284778,
          -23.414062490360944,
          -23.07733604145589,
          -22.745188337458533,
          -22.40847179134633,
          -22.067639686268684,
          -21.729226908949432,
          -21.386769694136664,
          -21.040769559214397,
          -20.694471211981465,
          -20.34868723300353,
          -19.999851501289555,
          -19.62008189513422,
          -19.27100073905224,
          -18.92638531991459,
          -18.588161684266517,
          -18.248324614771455,
          -17.91893082771564,
          -17.602343056242095,
          -17.283595867368387,
          -16.971013855715412,
          -16.682724384619622,
          -16.387549568085664,
          -16.09399970814327,
          -15.819904351598758,
          -15.53622841716392,
          -15.244803010467109,
          -14.96153412920028,
          -14.674097730402414,
          -14.384325343204667,
          -14.092251264932358,
          -13.794057665870046,
          -13.50353877170297,
          -13.21132811898712,
          -12.90482099173236,
          -12.60392219447869,
          -12.306052288733733,
          -12.000349963580295,
          -11.697178124530476,
          -11.39923804691345,
          -11.093392111059817,
          -10.785357285246695,
          -10.486092890232523,
          -10.18038877531292,
          -9.870093857162523,
          -9.569145551116153,
          -9.270163101591091,
          -8.971689287343583,
          -8.684948555769086,
          -8.396638712403725,
          -8.110775480521541,
          -7.828626245102295,
          -7.541759274591084,
          -7.25185419221323,
          -6.958716363996231,
          -6.667624138672746,
          -6.370607582327201,
          -6.064973734697458,
          -5.755738511435491,
          -5.444859257882132,
          -5.130587935937114,
          -4.817118437273158,
          -4.502311861517167,
          -4.192532975929694,
          -3.892115508842604,
          -3.592360289199098,
          -3.292157005112628,
          -2.994028767949145,
          -2.7072234297897504,
          -2.4156418234712964,
          -2.118372881667491,
          -1.826027837138399,
          -1.5372850622183543,
          -1.2428298103384017,
          -0.9422224484891255,
          -0.6552049888848881,
          -0.3802417472927005,
          -0.09499173291949081,
          0.18178537509938686,
          0.4336700157143668,
          0.6966730029626242,
          0.9665684353036693,
          1.216039652762898,
          1.4546975043632169,
          1.6925505536190624,
          1.9253051372526606,
          2.137269757080463,
          2.3348868282274555,
          2.541653755138296,
          2.7436144600862598,
          2.928477839467786,
          3.111118767816139,
          3.28909610967536,
          3.451869183628742,
          3.6096664019301143,
          3.757841920030514,
          3.893329687530655,
          4.019577932052728,
          4.13396385921677,
          4.229525363128095,
          4.311309889766212,
          4.380327916900443,
          4.432965936768186,
          4.475875460034202,
          4.507316137177971,
          4.521693504913679,
          4.519895939932456,
          4.50496611397356,
          4.47645575885916,
          4.43384802277373,
          4.374209266732488,
          4.296899117358691,
          4.210015616578304,
          4.104579242640396,
          3.9778396686966366,
          3.8420915834690517,
          3.692770841811775,
          3.5188157991922537,
          3.3386652503098957,
          3.145436982917815,
          2.933423991239192,
          2.7053988088309047,
          2.4672041042324535,
          2.2142547679138094,
          1.9470620857968879,
          1.6744119224200058,
          1.3940728617136626,
          1.1077367848826238,
          0.8120134386012675,
          0.5064169801305209,
          0.19600550427888197,
          -0.11519481997323494,
          -0.4348907632773606,
          -0.7601506912480445,
          -1.0811114512597637,
          -1.4113228395034298,
          -1.7520690288938887,
          -2.089199872100345,
          -2.4199960462935155,
          -2.754382843526987,
          -3.085879387873012,
          -3.403722679223684,
          -3.7287647344026817,
          -4.059303691707763,
          -4.371617495489478,
          -4.691167708791514,
          -5.0153341110063065,
          -5.325481016885064,
          -5.64444861472565,
          -5.973274399135193,
          -6.293507204356354,
          -6.622157004465535,
          -6.956470047111187,
          -7.285131106061637,
          -7.612929557778126,
          -7.952666481858264,
          -8.287211747780118,
          -8.619125852721707,
          -8.960351479197719,
          -9.292576089398906,
          -9.619806590711063,
          -9.949330091312321,
          -10.276437166767955,
          -10.605874630556425,
          -10.93603593512243,
          -11.260949741870894,
          -11.594693548760064,
          -11.926840393309933,
          -12.258285619429644,
          -12.59003510316944,
          -12.922628757236783,
          -13.25719101937559,
          -13.590107125337209,
          -13.925225829744729,
          -14.25991204836196,
          -14.596589257102645,
          -14.933226361922141,
          -15.30144852419057,
          -15.636389410093038,
          -15.951465822668757,
          -16.26585755696513,
          -16.582588739409395,
          -16.892811876290097,
          -17.208594370272603,
          -17.530849393175526,
          -17.844037896976886,
          -18.160160886264045,
          -18.490299225060138,
          -18.827149085965367,
          -19.159434910010802,
          -19.506458932281532,
          -19.86983306245915,
          -20.213055271598076,
          -20.558906850608093,
          -20.919337987116812,
          -21.268587445881664,
          -21.60575183614417,
          -21.94737843516884,
          -22.290350506575955,
          -22.60631395835898,
          -22.926389663624114,
          -23.241421946220758,
          -23.558718610991047,
          -23.877227033839514,
          -24.185953968542123,
          -24.496543399324647,
          -24.812914018277183,
          -25.129316218894648,
          -25.437705379813718,
          -25.76791426055,
          -26.1086499912129,
          -26.433932575197215,
          -26.762693636241615,
          -27.08976080996914,
          -27.41676910984239,
          -27.744558650908523,
          -28.06317597782058,
          -28.38813917833264,
          -28.709236052185172,
          -29.03603566656552,
          -29.364349086205472,
          -29.691810303017913,
          -30.0264406286328,
          -30.357478895900417,
          -30.690090074649092,
          -31.028524673395534,
          -31.359309213008196,
          -31.693658807808653,
          -32.0401146220198,
          -32.375413954350854,
          -32.711758407980135,
          -33.05302629626409,
          -33.386399455267714,
          -33.7226646869726,
          -34.05219298383436,
          -34.384159436675425,
          -34.71809821319222,
          -35.048326605006764,
          -35.38348081271346,
          -35.71592154712338,
          -36.03978343545733,
          -36.36951368666786,
          -36.69594528914535,
          -37.007635122277186,
          -37.32698354487897,
          -37.642807531478454,
          -37.94444818295919,
          -38.26191451116631,
          -38.58141482245345,
          -38.88234262194125,
          -39.20242173895554,
          -39.53072157932119,
          -39.83643879368301,
          -40.15298632538702,
          -40.47876182238641,
          -40.792606913290555,
          -41.1074698471274,
          -41.43679969125798,
          -41.756266158769215,
          -42.07473564083749,
          -42.43571142561871,
          -42.75501157154936,
          -43.069437724007486,
          -43.388043613914235,
          -43.7056555519817,
          -44.01925886767052,
          -44.34176130009067,
          -44.65919378166218,
          -44.98100341360274,
          -45.30894152180402,
          -45.639459898123164,
          -45.9704224177619,
          -46.30154149107646,
          -46.637379498865016,
          -46.97508382476037,
          -47.31025528614293,
          -47.64712673241311,
          -47.98848581612999,
          -48.32932923027304,
          -48.66487042474649,
          -49.004949800619414,
          -49.3396609641448,
          -49.6718517241719,
          -50.00484932992559,
          -50.335227267131884,
          -50.66062751044557,
          -50.98582505252587,
          -51.3167308698585,
          -51.637442071225024,
          -51.95570950852133,
          -52.27129218259571,
          -52.584435674414934,
          -52.89639499584523,
          -53.19971360181313,
          -53.50369647943074,
          -53.80834417268652,
          -54.11140527787669,
          -54.40502807821798,
          -54.701318235476705,
          -54.98525140774505,
          -55.254107245235,
          -55.53004044424332,
          -55.814750152120915,
          -56.090155152115344,
          -56.36012384614532,
          -56.64580452906922,
          -56.923991960855936,
          -57.19372426201853,
          -57.48081992941508,
          -57.769617907982806,
          -58.052444667673626,
          -58.34450638218545,
          -58.622731900421755,
          -58.89581824639618,
          -59.17753436912586,
          -59.456076332077735,
          -59.731547374587414,
          -60.009710603685875,
          -60.27995006956179,
          -60.54464623557332,
          -60.81164928851323,
          -61.07602994161075,
          -61.34739147355955,
          -61.62268296221908,
          -61.894212716288116,
          -62.16547747770566,
          -62.43832654566834,
          -62.70532729639679,
          -62.962695980546336,
          -63.2143876797705,
          -63.461203433044105,
          -63.68835902448967,
          -63.8982607904228,
          -64.0962428848378,
          -64.27117255867775,
          -64.42841844864822,
          -64.56614957216128,
          -64.67858233116108,
          -64.77163961435572,
          -64.84051860783873,
          -64.88591786395241,
          -64.91131741211484,
          -64.91549497820269,
          -64.89762703337516,
          -64.85853702847986,
          -64.80054349323746,
          -64.72698328290869,
          -64.63545030544971,
          -64.52517528059961,
          -64.40049610221821,
          -64.26059236617407,
          -64.10506466173719,
          -63.937213654748135,
          -63.75678927164039,
          -63.566809058558924,
          -63.36855105170832,
          -63.16123402630231,
          -62.94899136212532,
          -62.7301268465736,
          -62.5010241731829,
          -62.268705925559715,
          -62.03552164453808,
          -61.79876253720458,
          -61.56032905398105,
          -61.32510911069667,
          -61.0931423778431,
          -60.86006864423852,
          -60.633165719755844,
          -60.40872004894628,
          -60.18144368966343,
          -59.9611175572778,
          -59.7431854887936,
          -59.530374496683955,
          -59.32409536373215,
          -59.12345612818583,
          -58.931749710025315,
          -58.75193958763854,
          -58.57387741062418,
          -58.407209398167865,
          -58.25198632291714,
          -58.1041520483058,
          -57.95533131417458,
          -57.81408123244753,
          -57.68934364100779,
          -57.564041888593884,
          -57.44353670581038,
          -57.33216616877852,
          -57.22201936354363,
          -57.112527066628445,
          -57.012938936329114,
          -56.916896982928364,
          -56.821757929588095,
          -56.73343779055994,
          -56.646253679527824,
          -56.55991805279086,
          -56.479779242775436,
          -56.40156040638177,
          -56.32495433240671,
          -56.251541148571604,
          -56.181363015815705,
          -56.111733055739855,
          -56.04237249323248,
          -55.97368189380239,
          -55.90358060583399,
          -55.834298170582414,
          -55.765239957288266,
          -55.69592049313019,
          -55.62617783716715,
          -55.55531715660172,
          -55.48356508809312,
          -55.40993232303179,
          -55.33489601485874,
          -55.26098970759312,
          -55.186464063122216,
          -55.108746628010195,
          -55.03182396839522,
          -54.95389538313502,
          -54.87405565820421,
          -54.792608408457966,
          -54.70986707115987,
          -54.62217191944274,
          -54.53004390698982,
          -54.436522239332184,
          -54.336283692677746,
          -54.22972088121484,
          -54.120932249394386,
          -54.00617719260835,
          -53.887186620743236,
          -53.766120059154034,
          -53.63909351802302,
          -53.507983948645915,
          -53.37215650217293,
          -53.22543118442101,
          -53.07496935031896,
          -52.919581290765684,
          -52.753803225539556,
          -52.582938902895734,
          -52.41165765968816,
          -52.23312422864181,
          -52.04858353335398,
          -51.865090921062176,
          -51.673240496672385,
          -51.47490696095621,
          -51.28024641755678,
          -51.08386770926707,
          -50.87936304185,
          -50.67401180525247,
          -50.46888651295372,
          -50.250591510455315,
          -50.02824419922022,
          -49.805578279975435,
          -49.574271202122475,
          -49.345507768204705,
          -49.11341840103734,
          -48.87591231390753,
          -48.637064128921075,
          -48.39688987931705,
          -48.15138373981382,
          -47.905253414505076,
          -47.658117279444504,
          -47.41254890041668,
          -47.16761946594974,
          -46.917886867711196,
          -46.66774286714823,
          -46.418794773678584,
          -46.1662341543551,
          -45.90919209440135,
          -45.65125126255571,
          -45.39839301930402,
          -45.14891097286928,
          -44.89664578573406,
          -44.64640141712189,
          -44.40625758300676,
          -44.16035936869182,
          -43.91056736596237,
          -43.66787246329435,
          -43.42242805003103,
          -43.16835770344952,
          -42.91030981050776,
          -42.63774219963873,
          -42.358778181537346,
          -42.078747610712725,
          -41.80338575521076,
          -41.52490687245359,
          -41.24279741097451,
          -40.96427756356151,
          -40.685733453661385,
          -40.40558054494515,
          -40.130254405942274,
          -39.86757389533995,
          -39.60707938272576,
          -39.34475540998937,
          -39.07842460842025,
          -38.81931690041337,
          -38.562686853389096,
          -38.30266366588122,
          -38.04834798564219,
          -37.79954777962222,
          -37.55290773968637,
          -37.31669283965531,
          -37.08125179328632,
          -36.8423985289406,
          -36.59647282827979,
          -36.35043306474415,
          -36.107384064935566,
          -35.86479595362636,
          -35.61483890947434,
          -35.331083604078735,
          -35.08467593081306,
          -34.82106257777353,
          -34.54556572052031,
          -34.27460110941142,
          -34.003822190109645,
          -33.7234802213776,
          -33.44179473270728,
          -33.15404639354219,
          -32.87050327610256,
          -32.58059006720925,
          -32.27863778989865,
          -31.974910828643875,
          -31.625261336959714,
          -31.313387822712656,
          -30.99594893231147,
          -30.638295150715958,
          -30.307294264613517,
          -29.96915980473817,
          -29.630218779293614,
          -29.287615725836904,
          -28.949722701606397,
          -28.61214299684073,
          -28.263324125658396,
          -27.925086770255056,
          -27.568292044437335,
          -27.200004161191206,
          -26.841930786622143,
          -26.469623578292122,
          -26.10526166402949,
          -25.7633482883371,
          -25.412957223371198,
          -25.06886569338142,
          -24.73944990787778,
          -24.39985551461764,
          -24.06358432487452,
          -23.745255496146143,
          -23.426525335201283,
          -23.105885895095795,
          -22.799767638116997,
          -22.49727514661846,
          -22.191512596579802,
          -21.891550729953174,
          -21.590555095391352,
          -21.299800506744486,
          -21.007459721050708,
          -20.712505682578513,
          -20.417676359856692,
          -20.1288424114053,
          -19.846110724116734,
          -19.557595214382083,
          -19.28022537410284,
          -19.014449312268486,
          -18.750918995967762,
          -18.491107639453244,
          -18.235664351288477,
          -17.9795877790416,
          -17.721819734208616,
          -17.46897854981269,
          -17.214611409109313,
          -16.956473654155083,
          -16.695196476177763,
          -16.434045992582917,
          -16.167492560565577,
          -15.89800943709457,
          -15.6307679353881,
          -15.361289112735683,
          -15.092818270382255,
          -14.829004930418265,
          -14.562877850354946,
          -14.294519724502058,
          -14.030585803536798,
          -13.765237969926819,
          -13.497923111167285,
          -13.234891933479595,
          -12.97316886875696,
          -12.711808717546162,
          -12.454194391119383,
          -12.19602507631081,
          -11.935528952308767,
          -11.67958978903822,
          -11.421997715558938,
          -11.164448947544308,
          -10.911949175795565,
          -10.663612992465232,
          -10.410357865899986,
          -10.165148682321933,
          -9.924962021390026,
          -9.673653052987477,
          -9.432629859989227,
          -9.195342670726596,
          -8.948062321990827,
          -8.706241410623509,
          -8.47032010334807,
          -8.225928280604439,
          -7.978389168827798,
          -7.73736140804471,
          -7.497250189318121,
          -7.245795004371036,
          -6.9987034327101325,
          -6.757151653913929,
          -6.508834203192692,
          -6.263672595978965,
          -6.028150849844641,
          -5.78800386578519,
          -5.546046282574258,
          -5.314001026202576,
          -5.079433067953793,
          -4.841429196618071,
          -4.612694155697623,
          -4.388707178010669,
          -4.164553150775704,
          -3.9478262838874354,
          -3.7311509071527325,
          -3.522314335342655,
          -3.3124060115933043,
          -3.102505607858443,
          -2.893933689356671,
          -2.6813165678067397,
          -2.4716573725450317,
          -2.259457809256232,
          -2.0416601442580937,
          -1.820530332249989,
          -1.6011434418342279,
          -1.3792924671975615,
          -1.1573692093907881,
          -0.937683749914177,
          -0.7157838335096527,
          -0.5025761859928053,
          -0.29572698607465064,
          -0.06875462801314372,
          0.13916910940614716,
          0.3356064932076778,
          0.5254223494192539,
          0.7225861750073419,
          0.9174020765641653,
          1.109507283467813,
          1.296704119216514,
          1.4897693873692912,
          1.6818811947252001,
          1.8675234036787325,
          2.0493392212722954,
          2.237983491726821,
          2.426333618040964,
          2.603518075701454,
          2.785109481579425,
          2.971950526820138,
          3.146522955940648,
          3.308071412513028,
          3.466892579623205,
          3.6202023899320186,
          3.7542339221224283,
          3.8745624026034355,
          3.9968835226577486,
          4.111193097788245,
          4.210625589643177,
          4.303847746654786,
          4.389589899802569,
          4.463272747942096,
          4.527925739270417,
          4.581620827121556,
          4.623653373638112,
          4.653243214668194,
          4.667554863346527,
          4.66236752050303,
          4.638794262618646,
          4.598753633693416,
          4.545381036871401,
          4.476700932513723,
          4.389812718332553,
          4.287809094218327,
          4.169078151417449,
          4.0337891175561085,
          3.8853931955825773,
          3.7272593542819386,
          3.5507043988790468,
          3.358102237811909,
          3.1651740198986325,
          2.9526530684725723,
          2.7178985062406245,
          2.487766711156026,
          2.239010205724702,
          1.9697694841508335,
          1.7039840386279805,
          1.4275718050197304,
          1.1269846739476312,
          0.8222887596704817,
          0.5162959892493844,
          0.19558762207302433,
          -0.13345092285786847,
          -0.46220243878085393,
          -0.7929708493107742,
          -1.1214811859868086,
          -1.456120346240359,
          -1.7972115272559916,
          -2.1310910955781144,
          -2.4638837448918935,
          -2.8079759788362644,
          -3.1456326294461148,
          -3.4827274783486786,
          -3.8314926086555965,
          -4.180313251704143,
          -4.520758302292919,
          -4.865420412184198,
          -5.224967284992722,
          -5.56453732752588,
          -5.9000908168059025,
          -6.252465322458136,
          -6.5942883841183555,
          -6.92437217125159,
          -7.271789519182661,
          -7.612759287706714,
          -7.946660687609742,
          -8.294083993961767,
          -8.639737061587114,
          -8.980986481932046,
          -9.33242642784403,
          -9.689355404980818,
          -10.037825131094943,
          -10.39336751538966,
          -10.758525809216103,
          -11.119472443660197,
          -11.483530509935356,
          -11.855400525589813,
          -12.222370212220225,
          -12.587414867333706,
          -12.955518706677944,
          -13.32048479640778,
          -13.691787789490027,
          -14.054563710141634,
          -14.424951195143885,
          -14.79773534478032,
          -15.168355733815776,
          -15.537795644316514,
          -15.902878177737989,
          -16.276519065567175,
          -16.64688244976087,
          -17.0139208030353,
          -17.38706483478301,
          -17.76046386720403,
          -18.131722380813656,
          -18.49787495018238,
          -18.873141193368053,
          -19.245771525145923,
          -19.614272276698706,
          -19.987316216657533,
          -20.352476543605828,
          -20.71995251601444,
          -21.095355790849915,
          -21.460159884003456,
          -21.824294732196023,
          -22.208134791712077,
          -22.58507999968541,
          -22.94399072775922,
          -23.330385819325496,
          -23.718247852077766,
          -24.08400847274188,
          -24.463124366592318,
          -24.853688572998212,
          -25.22004139330868,
          -25.584441873185398,
          -25.97197836307736,
          -26.3415213744268,
          -26.709330811425424,
          -27.083419073826352,
          -27.458918687547662,
          -27.826383345452186,
          -28.19391321807642,
          -28.565180461751968,
          -28.94195519023841,
          -29.311238083351725,
          -29.670078650853863,
          -30.043955801452864,
          -30.41005097901917,
          -30.768999928936818,
          -31.12817167201201,
          -31.495659793925526,
          -31.85135437527981,
          -32.203436764856825,
          -32.56265543064982,
          -32.91970803545725,
          -33.28614455149576,
          -33.657117080737514,
          -34.03312542473182,
          -34.40593757281209,
          -34.782089260964156,
          -35.160448048017756,
          -35.52942898963792,
          -35.90658951585313,
          -36.284053145426775,
          -36.65476451632372,
          -36.99338940652855,
          -37.31210512684125,
          -37.63256930076928,
          -37.95244255152422,
          -38.2709995018038,
          -38.58830911084204,
          -38.90980292751436,
          -39.235710648118946,
          -39.5546493082041,
          -39.87375706460377,
          -40.22544316311305,
          -40.57636295198425,
          -40.92522886226912,
          -41.28364128623022,
          -41.62892987418175,
          -41.970592060306906,
          -42.332885121171934,
          -42.67804885782773,
          -43.01166281162483,
          -43.375288715268354,
          -43.70690286515323,
          -44.008154174490784,
          -44.33506079856576,
          -44.65807088043407,
          -44.96768244597823,
          -45.288473768435516,
          -45.616746242978365,
          -45.933603882916564,
          -46.25187139875348,
          -46.57454038621962,
          -46.90195673044048,
          -47.22911341441135,
          -47.55895709510095,
          -47.88997094675314,
          -48.21724850096846,
          -48.55122209291605,
          -48.88107824579509,
          -49.21569403871265,
          -49.54830345030725,
          -49.87465148645359,
          -50.2482872738873,
          -50.63216666433026,
          -51.01770219311104,
          -51.408769520926064,
          -51.797045291793914,
          -52.182119321516225,
          -52.568239582219334,
          -52.96108097928673,
          -53.35864888770875,
          -53.743459675795584,
          -54.102767939216626,
          -54.455600512326306,
          -54.80455211942588,
          -55.14372277795312,
          -55.49048522118435,
          -55.83989862934475,
          -56.17283974521251,
          -56.509396280707804,
          -56.84710967750188,
          -57.178233711388586,
          -57.52201949730945,
          -57.86756983068868,
          -58.21043608090959,
          -58.55772556251277,
          -58.908923038684364,
          -59.24408415654623,
          -59.589903375851506,
          -59.94478017125559,
          -60.28357890305282,
          -60.63399208769079,
          -60.9731898197203,
          -61.29241026263995,
          -61.61964823476025,
          -61.95298842315661,
          -62.27627181706702,
          -62.5982102760029,
          -62.92827500718808,
          -63.24779025502591,
          -63.57145526795926,
          -63.89032831139089,
          -64.19491538820286,
          -64.50695213099198,
          -64.81103198074504,
          -65.1021460453941,
          -65.38943664388782,
          -65.6736319905866,
          -65.95378645640052,
          -66.22419961020843,
          -66.4921635787646,
          -66.75574304226045,
          -67.01586461508562,
          -67.27312869486198,
          -67.52359827175695,
          -67.7743086078551,
          -68.01961465088993,
          -68.25347517935884,
          -68.48392426068527,
          -68.70910795234815,
          -68.91660496285618,
          -69.10380651804887,
          -69.28870781075972,
          -69.4631131754671,
          -69.61347619161562,
          -69.74508298029102,
          -69.86119938523795,
          -69.95423129069756,
          -70.02826179975484,
          -70.08163908860483,
          -70.1130964313865,
          -70.12406173747227,
          -70.11449531852482,
          -70.08527048680838,
          -70.0357871620045,
          -69.96704934908234,
          -69.87914884190009,
          -69.7715476923107,
          -69.64734699805649,
          -69.50868769106724,
          -69.35431046377643,
          -69.18477993135747,
          -68.99810414688947,
          -68.80065957254445,
          -68.58837086091653,
          -68.36380960860161,
          -68.13169619807452,
          -67.88819323818844,
          -67.63919346575103,
          -67.38659256982382,
          -67.12398807645634,
          -66.85931265224333,
          -66.59212419167349,
          -66.31643857753708,
          -66.04154184320969,
          -65.76644043859847,
          -65.48613485778944,
          -65.20650996423714,
          -64.92831577820456,
          -64.65198350368452,
          -64.37789680037756,
          -64.1026474637757,
          -63.83162052468435,
          -63.56478657311441,
          -63.29809115448759,
          -63.03285372895792,
          -62.77113047902272,
          -62.511150613610795,
          -62.25531030031971,
          -62.003569456359344,
          -61.75343602598804,
          -61.51444115870572,
          -61.278160381960305,
          -61.03960593492409,
          -60.81211536578428,
          -60.58713621924456,
          -60.36845116830578,
          -60.14320916898169,
          -59.92599679132155,
          -59.722507648154654,
          -59.511007719999085,
          -59.30449060217959,
          -59.108094248879965,
          -58.909046332347636,
          -58.70709589577023,
          -58.514498044683,
          -58.32689049259974,
          -58.136921933462474,
          -57.95387982162923,
          -57.77564527268614,
          -57.59574244302279,
          -57.421640918906036,
          -57.25399349987955,
          -57.0854261112508,
          -56.92234990475461,
          -56.75739418005345,
          -56.592720559580044,
          -56.429140883894625,
          -56.2626723178267,
          -56.094430525928125,
          -55.92663954394565,
          -55.76148150353939,
          -55.593551787433505,
          -55.42826123286333,
          -55.26383930916287,
          -55.09709569041535,
          -54.931617802966855,
          -54.76662284619,
          -54.600978613694224,
          -54.434320971781176,
          -54.27070783416176,
          -54.10205341065748,
          -53.930716891663565,
          -53.76328356334991,
          -53.58789387372266,
          -53.41189431824663,
          -53.23543668445821,
          -53.05269326341237,
          -52.86449025571554,
          -52.66952255601094,
          -52.4738294200348,
          -52.27044917585209,
          -52.05456234100216,
          -51.8355622979325,
          -51.60622529641284,
          -51.370920331434654,
          -51.13371546847616,
          -50.886162616523286,
          -50.6315265389719,
          -50.36893799545237,
          -50.095614436016305,
          -49.81196376832589,
          -49.5227464249609,
          -49.217725714497774,
          -48.90304716069872,
          -48.584201604977814,
          -48.252161304898735,
          -47.911745591341145,
          -47.56879187606734,
          -47.22700323391149,
          -46.83281146669143,
          -46.4702410093277,
          -46.11140104044296,
          -45.73978993127088,
          -45.36042460604,
          -44.98814678361028,
          -44.60845482629428,
          -44.22232453802405,
          -43.838346213926805,
          -43.45483175254206,
          -43.06529180331909,
          -42.67508983308675,
          -42.283880578380746,
          -41.890348995386525,
          -41.49409899762718,
          -41.09933547771172,
          -40.7021126832968,
          -40.30653402976841,
          -39.91086956691768,
          -39.514410149881066,
          -39.113402797902,
          -38.71511783247079,
          -38.31347119525082,
          -37.915177450093324,
          -37.51144414939198,
          -37.12041432120927,
          -36.731854876747136,
          -36.336325178616725,
          -35.94738466193311,
          -35.56846448153699,
          -35.17909068319027,
          -34.79419173563531,
          -34.41634416534482,
          -34.04013866541881,
          -33.66933543732716,
          -33.29934467389773,
          -32.946700682106496,
          -32.595723103600804,
          -32.23970053142105,
          -31.89297875313497,
          -31.54939915826174,
          -31.209228000500847,
          -30.874644803505756,
          -30.54571209305497,
          -30.24150487426131,
          -29.941264679434493,
          -29.65556353940081,
          -29.396640317655304,
          -29.13561070283149,
          -28.894534748036087,
          -28.669200199339638,
          -28.447210808479557,
          -28.24514897894562,
          -28.065695478182626,
          -27.884178456594803,
          -27.72121466335784,
          -27.580385557745,
          -27.441025464257606,
          -27.318037332251123,
          -27.213431769426453,
          -27.112569153891087,
          -27.02684243142981,
          -26.952040560013934,
          -26.89015793311576,
          -26.841657897848393,
          -26.799178365802046,
          -26.7623332112538,
          -26.73118256922781,
          -26.701813054921814,
          -26.672511431232987,
          -26.642687322170968,
          -26.61371163900235,
          -26.604725534031797,
          -26.597101359440742,
          -26.590344058134974,
          -26.583528825064608,
          -26.577574260168863,
          -26.572385492278176,
          -26.567331155802318,
          -26.562668454945392,
          -26.558620470762342,
          -26.555283737753275,
          -26.524395630462394,
          -26.490009498431338,
          -26.455113095080918,
          -26.419571657826847,
          -26.38342996200929,
          -26.346678757884227,
          -26.309309285749165,
          -26.271418137912175,
          -26.232468054980703,
          -26.192622671193412,
          -26.182885579595844,
          -26.176561889525477,
          -26.170019220735703,
          -26.163518676255148,
          -26.157031284645136,
          -26.15037816272362,
          -26.143791394631844,
          -26.137149470624433,
          -26.130435039069834,
          -26.12369410297835,
          -26.100864735902903,
          -26.0762011588705,
          -26.051429206960446,
          -26.026699805734967,
          -26.001949247406344,
          -25.977174709685514,
          -25.95241373081624,
          -25.927620255904582,
          -25.90281436231869,
          -25.87792048986312,
          -25.86912552068418,
          -25.861938869545675,
          -25.854678826415526,
          -25.847514306923753,
          -25.84043267225333,
          -25.833185235135094,
          -25.825912260874038,
          -25.818712461828877,
          -25.811343661510133,
          -25.804032062722534,
          -25.76327200353828,
          -25.71816951961668,
          -25.67309950738135,
          -25.6282189769851,
          -25.58362563075885,
          -25.539095963918186,
          -25.494459405581956,
          -25.45004414705182,
          -25.40584975898497,
          -25.361193146420717,
          -25.35176083098965,
          -25.346356673412064,
          -25.341087701934505,
          -25.33606270204788,
          -25.331045020776386,
          -25.326051648671193,
          -25.321001702151786,
          -25.315407894826496,
          -25.310270117846283,
          -25.305238426422218,
          -25.30388068436576,
          -25.302596981996626,
          -25.301515761725618,
          -25.300424963503286,
          -25.299121605821288,
          -25.29786948141474,
          -25.29672765150048,
          -25.295533260114343,
          -25.294258667253228
         ],
         "xaxis": "x",
         "y": [
          45.300763999112,
          45.301341573551824,
          45.30202395222192,
          45.3027304682885,
          45.30322237079558,
          45.30362067496451,
          45.304425203332364,
          45.30514048380767,
          45.30604976529649,
          45.306832191191525,
          45.30756898223068,
          45.30846231208834,
          45.30938864992191,
          45.310146673033415,
          45.31089687456964,
          45.31180081847361,
          45.312637714650506,
          45.31349301157287,
          45.314073695195525,
          45.3146608251378,
          45.31527304638943,
          45.31595919671405,
          45.31653792238171,
          45.317194737096244,
          45.317770872862425,
          45.318388003341866,
          45.31896967467463,
          45.31946843250839,
          45.319930227441446,
          45.32043543954677,
          45.32082272659343,
          45.32121324116136,
          45.32163620609007,
          45.32203450106808,
          45.32252305614339,
          45.32297280120289,
          45.32336242467605,
          45.32369386666636,
          45.32409141971895,
          45.32452122201855,
          45.324815845330846,
          45.32521256200015,
          45.32573437392582,
          45.32601426487314,
          45.326272186092524,
          45.32656776983637,
          45.32694553337056,
          45.327221708071704,
          45.32751804238648,
          45.32788106789423,
          45.328215034350976,
          45.328615342235956,
          45.3290091977588,
          45.32931759406239,
          45.329637175733765,
          45.32995418467703,
          45.33032833395729,
          45.33064009395056,
          45.330855206546445,
          45.33118968061984,
          45.331416453200255,
          45.33172398395247,
          45.332056224367435,
          45.33230550243798,
          45.33257395929481,
          45.3328823693904,
          45.33316931701505,
          45.33381599455605,
          45.334690400214996,
          45.33548640314393,
          45.33624919080267,
          45.33717076976769,
          45.33816451158525,
          45.3390484876764,
          45.3398846550109,
          45.340815079256465,
          45.34185668623101,
          45.34257141177747,
          45.34332312698853,
          45.344146460405405,
          45.34477346199053,
          45.345522978248866,
          45.346439532787365,
          45.347170382318076,
          45.347866414668964,
          45.348793914547244,
          45.349654386282666,
          45.350600302806356,
          45.351696416438095,
          45.35275943072291,
          45.35380572241721,
          45.35478027689853,
          45.35578104718409,
          45.356854446587434,
          45.35785394410009,
          45.35885438676964,
          45.359800413158574,
          45.36070616051463,
          45.361356618172934,
          45.36193783590679,
          45.36270764202978,
          45.36344215343657,
          45.36395524598705,
          45.36452216407602,
          45.36500010695263,
          45.36572464375114,
          45.366549414871706,
          45.36715644301529,
          45.36788206871917,
          45.36860188969828,
          45.369307664419,
          45.370158507472766,
          45.37094808765331,
          45.371596244630965,
          45.37230734145343,
          45.373077006469224,
          45.37390746412289,
          45.374738978946525,
          45.37533094086246,
          45.375911926393584,
          45.376660790566646,
          45.37744844505151,
          45.378120337993614,
          45.37871281301936,
          45.37944455726284,
          45.38024740126725,
          45.3810150092614,
          45.38159616835665,
          45.38201869243848,
          45.38272884241276,
          45.383487249053935,
          45.38398497519398,
          45.3845992105842,
          45.38542582840918,
          45.385949363001984,
          45.38680492486659,
          45.387348537977445,
          45.38784484606646,
          45.3881401319806,
          45.3888083451927,
          45.38951797313852,
          45.389847682969375,
          45.39038062223386,
          45.39101432104074,
          45.39166716937402,
          45.39244323096255,
          45.39311681660571,
          45.393629975075534,
          45.39436923588978,
          45.39544047566005,
          45.395946607659376,
          45.39644577388547,
          45.397136851800866,
          45.39787944394874,
          45.39851183408501,
          45.39897565687679,
          45.399340275298286,
          45.39963115185406,
          45.40028360093086,
          45.40084689773852,
          45.40120478758708,
          45.40159750972863,
          45.40224271477849,
          45.403056398790575,
          45.4041792694118,
          45.4047000889682,
          45.40520158629604,
          45.406105313965924,
          45.40748144561115,
          45.40943529834741,
          45.4107837640198,
          45.4118891588229,
          45.41348431974955,
          45.41515658983633,
          45.41667919460014,
          45.41818121451507,
          45.419703865894896,
          45.42113282745641,
          45.422553061774046,
          45.42405415464268,
          45.42544418832713,
          45.4268120040987,
          45.42827202741131,
          45.42979469260146,
          45.43121034271308,
          45.43272739895048,
          45.43424778583486,
          45.43546298459962,
          45.43645932152596,
          45.437592945562,
          45.43890910745662,
          45.44024249061596,
          45.44149552216681,
          45.44242302356497,
          45.44350379303764,
          45.44477792418805,
          45.445957075912965,
          45.447009319383746,
          45.44778973119988,
          45.4487710307042,
          45.45007783625308,
          45.45090763042639,
          45.45183603800033,
          45.452948351405226,
          45.45438467008537,
          45.456721755917506,
          45.45818512008324,
          45.46038379692406,
          45.462409788324116,
          45.46436920738667,
          45.47031123502449,
          45.48198682975995,
          45.50236060450161,
          45.53412777155301,
          45.57865482102878,
          45.63461195057368,
          45.69618820418663,
          45.75575362855735,
          45.805235963722915,
          45.844574314502026,
          45.87319009501468,
          45.89457350099864,
          45.90985702727797,
          45.920426784645194,
          45.929714314741986,
          45.94102433941112,
          45.95754900248294,
          45.984717098417015,
          46.02364689867042,
          46.074959813766874,
          46.1392187367292,
          46.21581309604001,
          46.303513964077254,
          46.402348322939716,
          46.51232170450343,
          46.63443683273643,
          46.769414650239135,
          46.91620833647572,
          47.072472510197336,
          47.23593432263914,
          47.40689313834542,
          47.58589559174276,
          47.76674702509741,
          47.94743119221877,
          48.12661549200032,
          48.306004856275344,
          48.48083176129356,
          48.64841047310979,
          48.813218898197654,
          48.96797914345479,
          49.11114843563967,
          49.24810402015948,
          49.373442983020205,
          49.48679746006202,
          49.586225276514554,
          49.67486678418323,
          49.75045581871038,
          49.80942562458604,
          49.85397554296133,
          49.88507842427781,
          49.90085090313507,
          49.8988757650409,
          49.87742261138937,
          49.83738247164229,
          49.77929693160578,
          49.70297245886327,
          49.60700749450082,
          49.49412270164788,
          49.36899891548721,
          49.22287365957846,
          49.0576477713906,
          48.89487209314991,
          48.706037434197974,
          48.49781142868888,
          48.28055252354111,
          48.04992989325078,
          47.8121765846866,
          47.559256286586965,
          47.28776340821796,
          47.02643650298985,
          46.75156963194857,
          46.45689980375514,
          46.17250442856052,
          45.880475804042035,
          45.57019228703469,
          45.260523105678715,
          44.94878994030538,
          44.62878206191175,
          44.299830325210415,
          43.969893204712456,
          43.63593348642329,
          43.29485327305683,
          42.95872002652995,
          42.61912286071814,
          42.26607771350164,
          41.918973232819475,
          41.57098241775734,
          41.214255254373604,
          40.8400237615168,
          40.48499485985969,
          40.123055774101914,
          39.741634268528905,
          39.369172624470124,
          39.003215264536074,
          38.62717062932619,
          38.24212774832719,
          37.877598836186976,
          37.504685485908134,
          37.117251461184125,
          36.74198424369736,
          36.37754675140968,
          35.99923365132266,
          35.6264236219529,
          35.266323625486265,
          34.894081708392854,
          34.52563453098432,
          34.15414418512981,
          33.78913023990528,
          33.41842289323424,
          33.0435961836081,
          32.679323999198324,
          32.31371279496165,
          31.95437866296702,
          31.580268678266055,
          31.229479177704786,
          30.877781472263738,
          30.508994931523873,
          30.150488891931595,
          29.796302517436125,
          29.44027879747006,
          29.074791931980396,
          28.712191780253157,
          28.35823855229896,
          27.99879545077412,
          27.640204060378316,
          27.28388283528901,
          26.92919627599728,
          26.56984937023628,
          26.21602342567307,
          25.863629406629126,
          25.49790648584417,
          25.149619176401096,
          24.804710592355164,
          24.445104311412454,
          24.09022404913823,
          23.745532269319668,
          23.3857846839867,
          23.03166683343009,
          22.683762062252573,
          22.329872038849924,
          21.989574640144735,
          21.64845920134522,
          21.3049796381533,
          20.97282416491729,
          20.64203158943567,
          20.30090176762072,
          19.973057305957397,
          19.645640435661452,
          19.30615980903741,
          18.980915208503788,
          18.65644862255679,
          18.324743966065398,
          18.00053865051007,
          17.6797624591609,
          17.34690612817321,
          17.01408542910839,
          16.689982779726076,
          16.358375758321905,
          16.028560988784907,
          15.705030884331155,
          15.38325393302482,
          15.057322482131829,
          14.731575851703301,
          14.405003248468422,
          14.078159797923878,
          13.74599436158187,
          13.415915683022071,
          13.085144947087308,
          12.74771355257983,
          12.414912886241646,
          12.079091946567505,
          11.738366338724818,
          11.402272003387672,
          11.069875069462155,
          10.72966346850544,
          10.39148332303563,
          10.064162846394513,
          9.69618110173987,
          9.35931374486956,
          9.033307291371546,
          8.70745863235564,
          8.37898415672725,
          8.056761112476863,
          7.739709332572376,
          7.421201950111207,
          7.105714426783437,
          6.792744303735408,
          6.476676019972183,
          6.16768207838867,
          5.852895579209107,
          5.532391193871351,
          5.218912864659064,
          4.900400654136906,
          4.569876849158174,
          4.243970598084207,
          3.924903130447823,
          3.587176721825192,
          3.258867782658453,
          2.942791882605584,
          2.6042377728092205,
          2.2705783121379435,
          1.9487151348600342,
          1.6112175295461257,
          1.2761688946705378,
          0.9508632327376363,
          0.6175763442038749,
          0.299787417162958,
          -0.015741272825973762,
          -0.3367256025240243,
          -0.6371876578615306,
          -0.9383847043225775,
          -1.2456306620029711,
          -1.534783750817155,
          -1.824882339729615,
          -2.1213194813266765,
          -2.401357524525755,
          -2.6794150779470147,
          -2.9543812881729097,
          -3.2198376847186516,
          -3.4748461696052937,
          -3.7234681836955463,
          -3.9416898458483063,
          -4.140137812307389,
          -4.335503896360229,
          -4.506983229102717,
          -4.653251207477817,
          -4.785819888437005,
          -4.892279273068619,
          -4.971537682661272,
          -5.030458988709827,
          -5.0658188226727106,
          -5.076422764936061,
          -5.06262634071044,
          -5.026330897488161,
          -4.969686300691085,
          -4.891492372832748,
          -4.794552814995628,
          -4.679509821705779,
          -4.547120899746603,
          -4.399614625795304,
          -4.2381700837055165,
          -4.060430777530634,
          -3.872435638632237,
          -3.6710308450176057,
          -3.455488028949548,
          -3.231469231772502,
          -2.9966344842292423,
          -2.750927800489316,
          -2.500916583739034,
          -2.2463141385572807,
          -1.9876805600808203,
          -1.7266430581510566,
          -1.467889712456801,
          -1.2097227199180942,
          -0.9528219875076482,
          -0.6979055196300923,
          -0.44600551231092733,
          -0.19535390779521317,
          0.0541737457367337,
          0.29400326611414,
          0.5246764581160047,
          0.7539626589974129,
          0.9736166714470532,
          1.183989511360528,
          1.3937315750387254,
          1.6019416405285407,
          1.7895440011700536,
          1.973619328412509,
          2.1577995839358044,
          2.325366460938859,
          2.4929312307479226,
          2.6590554482926407,
          2.8080533697417174,
          2.9546256424311856,
          3.09969079163285,
          3.2335468937711505,
          3.3675130495414747,
          3.4992067476044464,
          3.6153651176217334,
          3.7264172791652688,
          3.8410242036315507,
          3.9478917310532426,
          4.049599274189725,
          4.156343028680598,
          4.258484815993488,
          4.35249002831893,
          4.450333333872016,
          4.5488629889563565,
          4.644884540423524,
          4.7460562127469785,
          4.849951616982029,
          4.955035466070503,
          5.066187722650232,
          5.179325060094688,
          5.2933875761899545,
          5.409626084324819,
          5.525889405780967,
          5.642460132379497,
          5.7631433440158,
          5.8852648342585745,
          6.011591942119079,
          6.144150940208226,
          6.284841345766752,
          6.431223582187876,
          6.583792196588058,
          6.743078809517763,
          6.9092906576273,
          7.0803177541799975,
          7.259502022852225,
          7.445945586695279,
          7.640928060221949,
          7.843238411397529,
          8.053057626660687,
          8.268415734705762,
          8.490396816861495,
          8.71891837463856,
          8.951769237822816,
          9.193218471325817,
          9.442594924647457,
          9.696365138125932,
          9.951458576255341,
          10.2120316761229,
          10.47864708607293,
          10.74647204211657,
          11.018385315278776,
          11.29279184675726,
          11.574945542225109,
          11.863286704760498,
          12.142861947700974,
          12.424984275096996,
          12.717908216058275,
          13.006249798999773,
          13.298788519143722,
          13.598894208518637,
          13.900405695370429,
          14.197368082720658,
          14.495312996367689,
          14.796948313285007,
          15.097945170890185,
          15.401355532178915,
          15.717805881010413,
          16.031520095830437,
          16.339101788283934,
          16.660392023315495,
          16.98159027411665,
          17.292653640261246,
          17.62171122712807,
          17.94892979037467,
          18.26922667115353,
          18.607125469156045,
          18.947401080835,
          19.276079319682413,
          19.623698553925163,
          19.96987188612568,
          20.304282776178955,
          20.656754005979543,
          21.0056343233842,
          21.339355562931917,
          21.684092928221315,
          22.01573036490737,
          22.348805633718737,
          22.6912983917052,
          23.02687460807076,
          23.356656517438864,
          23.684969813497123,
          24.003146095679078,
          24.321778792664468,
          24.651032913031717,
          24.969136693301518,
          25.29591867506696,
          25.62612936076743,
          25.94017776058608,
          26.26113290602105,
          26.588280217576173,
          26.895463290126933,
          27.222442340904838,
          27.55559214430204,
          27.87267187562141,
          28.197921036197673,
          28.525211405628266,
          28.844795525491932,
          29.15258188034745,
          29.466937726573722,
          29.776639528891486,
          30.079641033751738,
          30.382562678840582,
          30.67124595352575,
          30.958424296196142,
          31.247475362821486,
          31.528198961981687,
          31.80750159283566,
          32.080281832540074,
          32.35177729430272,
          32.62700611360116,
          32.89722613195348,
          33.17331291032348,
          33.460902140624334,
          33.73481415623733,
          34.02158170641768,
          34.32815902776748,
          34.625095195773504,
          34.931117235726944,
          35.26233505594226,
          35.57873292326579,
          35.877764386430236,
          36.20052486048117,
          36.52870849117942,
          36.840537392162716,
          37.1641226831591,
          37.49705722422052,
          37.81708695838772,
          38.13578681251307,
          38.457874553223824,
          38.775614575292884,
          39.093632399009046,
          39.411178747966616,
          39.7306961729037,
          40.05736051603555,
          40.38362133088337,
          40.703220569224996,
          41.02848519872867,
          41.35634815781767,
          41.67736377855218,
          41.995194193616534,
          42.318129957180716,
          42.634178551730514,
          42.922966851131626,
          43.21012264796641,
          43.5040655962893,
          43.76851481772789,
          44.02912724506593,
          44.305809205144826,
          44.5622250376899,
          44.807167150442936,
          45.06652071998439,
          45.31847297765649,
          45.566011133706276,
          45.826348969099065,
          46.08277850217597,
          46.33411551433679,
          46.58967771135485,
          46.84386762530234,
          47.09700246169205,
          47.35236193546806,
          47.60960216206434,
          47.86561418904249,
          48.123268741192796,
          48.37724558753112,
          48.63188397938058,
          48.88512811945823,
          49.143508878831206,
          49.39835903392802,
          49.656066115959796,
          49.91621165051497,
          50.17140426357718,
          50.41941225470457,
          50.674403029351495,
          50.91252439281616,
          51.14230275477052,
          51.379739937707136,
          51.60407313386915,
          51.8252709936769,
          52.05510728411453,
          52.27507903289203,
          52.49084093094618,
          52.734194896018536,
          52.954018978760715,
          53.170265300558725,
          53.391621328731794,
          53.61890214033733,
          53.83936786363542,
          54.05733100184072,
          54.27972415894159,
          54.49766515626916,
          54.71125855539906,
          54.92970282110391,
          55.147510230894326,
          55.357281099974635,
          55.57150256122695,
          55.78735713927546,
          55.994838066916536,
          56.20139326980965,
          56.40601719777533,
          56.60065735462683,
          56.79619626417855,
          56.98765507374571,
          57.17496351274691,
          57.36379561508075,
          57.552068230944016,
          57.742561532166434,
          57.93062053298537,
          58.12005092905921,
          58.315121889807656,
          58.51253401279553,
          58.71188199346526,
          58.911383893579085,
          59.11169764875003,
          59.31360008885097,
          59.5135060053731,
          59.7092070119636,
          59.90291608059877,
          60.0988785380776,
          60.293137574580925,
          60.48408287785949,
          60.67705457418497,
          60.872691351526996,
          61.06911697752726,
          61.26693973907211,
          61.463619659666705,
          61.67057237188686,
          61.873395305031416,
          62.06994071190517,
          62.2763117136212,
          62.48288569573003,
          62.670433806439334,
          62.86599398885605,
          63.06484624294453,
          63.23994309585581,
          63.404790257604844,
          63.5683951546275,
          63.71266402266976,
          63.833313673297184,
          63.957343197384354,
          64.07253337240147,
          64.16632664101635,
          64.25151881995679,
          64.32572991848842,
          64.38285729196312,
          64.42834672854003,
          64.46234364646841,
          64.48363245449228,
          64.48974560572483,
          64.47974511722353,
          64.45367193180653,
          64.41272649008886,
          64.35915170182273,
          64.29585728147505,
          64.21908416931414,
          64.12905525277463,
          64.02759206304033,
          63.91155210481026,
          63.783250461016685,
          63.645608893204916,
          63.49812769160795,
          63.33528536342317,
          63.16492904610628,
          62.98892398285202,
          62.795741138748994,
          62.58970387725575,
          62.38259767718872,
          62.160179037963886,
          61.923620482714576,
          61.68293145375927,
          61.42330628791671,
          61.15519230296776,
          60.876331872212845,
          60.579762295680354,
          60.275645768282175,
          59.960507387483716,
          59.63703073309107,
          59.30850704074147,
          58.9757028791477,
          58.63870745665814,
          58.29540932396677,
          57.95444873224277,
          57.61173711178277,
          57.267852354424896,
          56.92859530487275,
          56.590442033230566,
          56.25305986809595,
          55.912764342101134,
          55.56525941998776,
          55.21658153469502,
          54.879889471452486,
          54.53606114761929,
          54.184080384793454,
          53.85109730890776,
          53.50880070604252,
          53.15899468183553,
          52.814462304514855,
          52.48064377041907,
          52.13777724028534,
          51.79654702573489,
          51.46687954964362,
          51.1266105774489,
          50.784511846951915,
          50.451770742434185,
          50.111797708303484,
          49.76748946434314,
          49.425916171246854,
          49.08613195209399,
          48.736427537896795,
          48.3856070070895,
          48.04055301139471,
          47.68508895813121,
          47.33024274544863,
          46.98171587327677,
          46.633615480805815,
          46.2880205583211,
          45.94400735137217,
          45.59217569410682,
          45.25079461473036,
          44.90637087473837,
          44.55294148523616,
          44.205832777584554,
          43.85722484736744,
          43.50834110350364,
          43.1621088257624,
          42.81560345410025,
          42.46566436746404,
          42.118339414714214,
          41.77312931554235,
          41.41987859061167,
          41.073298559779715,
          40.72837872280661,
          40.3770253694961,
          40.02904833041153,
          39.68835985233569,
          39.34439804680693,
          39.009829973197114,
          38.671687745887205,
          38.323374457630734,
          37.98897010516161,
          37.65242926201179,
          37.304928825636814,
          36.95080862383974,
          36.61504655523721,
          36.26367204319447,
          35.89855452154007,
          35.544102364865196,
          35.19010380073074,
          34.83320667240535,
          34.46870627907129,
          34.120882613512286,
          33.771363807673204,
          33.41198798673348,
          33.06219420676293,
          32.712277566591176,
          32.36035455047789,
          32.00757065696203,
          31.661419421657694,
          31.315557458592334,
          30.9647625575405,
          30.617965955180733,
          30.265302718072977,
          29.919287077307345,
          29.571155743794343,
          29.216495853346082,
          28.878197989565503,
          28.536667325767418,
          28.190942579958637,
          27.845283287699914,
          27.513155173991645,
          27.179098623728564,
          26.83502343895677,
          26.46103637376922,
          26.124888471057403,
          25.779048125633576,
          25.42333823469573,
          25.069760328006527,
          24.72118898254519,
          24.36798861523095,
          24.015711997513932,
          23.668584379139066,
          23.315293198737912,
          22.961272806670213,
          22.610807753387963,
          22.2674733006515,
          21.91722673210496,
          21.567342437432803,
          21.233823479248375,
          20.892896771613447,
          20.544384009259172,
          20.20672800387583,
          19.866889099097538,
          19.512059752683733,
          19.170635603647817,
          18.836611494522998,
          18.484065621800763,
          18.143236322521165,
          17.81514553870242,
          17.469667809468664,
          17.131528575343008,
          16.809030674807882,
          16.466696872242288,
          16.1214317762364,
          15.799733330298245,
          15.42877363811099,
          15.073792858668515,
          14.747406156504846,
          14.414222581446774,
          14.063486594190591,
          13.729510593899505,
          13.395417648581581,
          13.048103444311565,
          12.706091630874697,
          12.364460809725964,
          12.015689641799408,
          11.669290615538904,
          11.324334069605856,
          10.979868486367371,
          10.640546596943121,
          10.298037572697554,
          9.953989503168742,
          9.612220302018773,
          9.267630755042081,
          8.921786546643382,
          8.575497419945757,
          8.237742897424031,
          7.88943212755558,
          7.5431838368751745,
          7.201932616872471,
          6.851825258506718,
          6.5029603902480995,
          6.154858315440672,
          5.803513795390799,
          5.448087318478452,
          5.096922909884843,
          4.7471486112752075,
          4.394007854240869,
          4.040519825603647,
          3.690172063167879,
          3.3392603502264295,
          2.9851205498345794,
          2.6333955725056244,
          2.288299469792739,
          1.9398064120443241,
          1.5997071035704864,
          1.2659347793408662,
          0.934825270517099,
          0.6058723220959414,
          0.28230350527672887,
          -0.03629015797928825,
          -0.36071636564953935,
          -0.6819547254777746,
          -1.007643085546778,
          -1.330066825079602,
          -1.6492567694716918,
          -2.0104130703536005,
          -2.339223859536039,
          -2.6558284693529974,
          -2.9752868315982397,
          -3.3033092125038506,
          -3.6322167726085306,
          -3.950657289158474,
          -4.274167227651788,
          -4.601383622381596,
          -4.915750468997668,
          -5.23600751664346,
          -5.555412012664591,
          -5.847173310532583,
          -6.142911390226606,
          -6.444978920109589,
          -6.72613985268185,
          -7.001156311358316,
          -7.279213081058419,
          -7.544352527749074,
          -7.804971727588198,
          -8.061597996276314,
          -8.310382291110322,
          -8.554022006119533,
          -8.797213336289916,
          -9.03321605866088,
          -9.26882078620251,
          -9.497978440377171,
          -9.719132779090145,
          -9.931711355256954,
          -10.134639615353883,
          -10.327031589724083,
          -10.49394959295115,
          -10.638262924931626,
          -10.769628023409727,
          -10.879246376242422,
          -10.964817519121414,
          -11.032428862255294,
          -11.079372097718194,
          -11.102912315321094,
          -11.103191905368893,
          -11.079244514526284,
          -11.032721627638416,
          -10.961261277617764,
          -10.865196952237048,
          -10.74901918697948,
          -10.61000961740642,
          -10.449652153407792,
          -10.278802388244747,
          -10.086174464728362,
          -9.874521154196852,
          -9.65770029887742,
          -9.423675235606092,
          -9.174134318110932,
          -8.921988604113233,
          -8.656989114942014,
          -8.380594650253201,
          -8.098963878941928,
          -7.8108678727576075,
          -7.514900432821215,
          -7.214406717186254,
          -6.91193496707461,
          -6.60380849731807,
          -6.293174592930257,
          -5.982330019792183,
          -5.672116824982232,
          -5.3652697050718325,
          -5.058392164619464,
          -4.75748769823338,
          -4.459446086908367,
          -4.161658500314655,
          -3.868079626007064,
          -3.576863053064497,
          -3.286606466411095,
          -3.001645623116065,
          -2.718640927432209,
          -2.4422744920606325,
          -2.1746787881673773,
          -1.9016214411074897,
          -1.6379852872735574,
          -1.3794056948426807,
          -1.1263237319579624,
          -0.8645465683249527,
          -0.6089902795573999,
          -0.3723638395152906,
          -0.12509393518272546,
          0.12003648106456932,
          0.3505740876000286,
          0.5846856719358533,
          0.8244867863742374,
          1.0491993902429702,
          1.2699963556370675,
          1.496821911062356,
          1.712503717279573,
          1.9248968578725032,
          2.1418482701366557,
          2.3505439599106426,
          2.5523825862884832,
          2.7531995300117607,
          2.9541553860330523,
          3.148465256215704,
          3.3398151305240726,
          3.5299514440337405,
          3.720296770847451,
          3.9053071456439357,
          4.088881914933927,
          4.276781445025462,
          4.462576188309582,
          4.646870384206813,
          4.835697821217075,
          5.029821917521804,
          5.221367644332071,
          5.415360946106958,
          5.615232463589128,
          5.8090913345269435,
          6.004986928654759,
          6.203827654982399,
          6.4006922122688,
          6.600285224867596,
          6.801033264701665,
          6.999531515865841,
          7.202487639332157,
          7.410785615382285,
          7.618194445673296,
          7.8305529639776355,
          8.048794527824265,
          8.269230040416549,
          8.494515105781907,
          8.726845100344663,
          8.961369651981645,
          9.1967088366889,
          9.440421022370094,
          9.682894032455827,
          9.932018824589539,
          10.192585984206067,
          10.45695130453579,
          10.725620750180626,
          11.009196295992373,
          11.295492970999367,
          11.582235534121276,
          11.878578270279743,
          12.182832393582968,
          12.479401710417404,
          12.782775167320377,
          13.094100571366237,
          13.400245911423351,
          13.70514648225263,
          14.017984705260282,
          14.33212251738247,
          14.639618146964136,
          14.95767547988323,
          15.278803640425702,
          15.596193195655003,
          15.922162557440148,
          16.251956920872253,
          16.57167234279722,
          16.89829409490034,
          17.232586891473908,
          17.566312071722997,
          17.899789800152938,
          18.242636362853847,
          18.5874319540848,
          18.930956278371266,
          19.271359875226974,
          19.61471393570453,
          19.96071653519306,
          20.305240607722805,
          20.648476213008024,
          21.000160129295892,
          21.357801222709778,
          21.707692400950048,
          22.056525876511053,
          22.415288221263225,
          22.771383305433954,
          23.116170563384895,
          23.473800779097594,
          23.83402006978679,
          24.184389383985415,
          24.543669015913185,
          24.911485261810032,
          25.27403401822014,
          25.635177289261257,
          26.01004795898074,
          26.378335243972316,
          26.738358933747435,
          27.113709043417835,
          27.49072739057218,
          27.8531538233007,
          28.221658491015777,
          28.595727293922245,
          28.95637169156403,
          29.32204101295745,
          29.69621141381072,
          30.060466513854657,
          30.423735098723874,
          30.787978494030376,
          31.145739588431468,
          31.493882032695705,
          31.842876111156787,
          32.197179154784145,
          32.54672086652207,
          32.8969536154289,
          33.25853532862679,
          33.609723337002855,
          33.94989446641682,
          34.30025212183056,
          34.65264409337346,
          34.98888831453011,
          35.32804279011438,
          35.67547524302361,
          36.00724974720602,
          36.331694431613094,
          36.66466942998067,
          36.98040335169968,
          37.298097905182736,
          37.61034756605825,
          37.90347642595841,
          38.199572829167074,
          38.48304663331545,
          38.758875029184075,
          39.05150458495746,
          39.3213311417734,
          39.58277083626067,
          39.8598149615599,
          40.13442464859941,
          40.40846823880898,
          40.687878257587755,
          40.96034686903057,
          41.2423625928913,
          41.531887678961525,
          41.823000836541055,
          42.108567927464875,
          42.41160627488574,
          42.710933013990775,
          42.99896832353256,
          43.305438515642486,
          43.61473659522926,
          43.9075228194131,
          44.2195852489998,
          44.52088858915054,
          44.775271618516086,
          45.038717568139646,
          45.3065147252586,
          45.558644558606005,
          45.806638154774696,
          46.05744570682455,
          46.297726955338895,
          46.53007589812538,
          46.75860788541654,
          46.98314649371935,
          47.21337823270735,
          47.43538870321986,
          47.65098488001414,
          47.86296819613546,
          48.07196452474747,
          48.27752789194195,
          48.4727917742563,
          48.671171000903946,
          48.870510506147575,
          49.068556827284254,
          49.26864223170053,
          49.4664655137866,
          49.66602445581489,
          49.85699306272575,
          50.04159151962469,
          50.22139204221718,
          50.39857397772692,
          50.56968175498876,
          50.743227400695744,
          50.914436488115655,
          51.07572512908874,
          51.2374188274606,
          51.400640247005846,
          51.56264390234506,
          51.72376071170347,
          51.887448023861666,
          52.050670372454405,
          52.21163653428425,
          52.37272718456936,
          52.530928525770655,
          52.69368258186714,
          52.85693113087273,
          53.01673973310257,
          53.175978871665535,
          53.33413338044323,
          53.488898307705625,
          53.641953059592616,
          53.794997423257534,
          53.94614986829016,
          54.09821763981167,
          54.24763872281109,
          54.39556974514787,
          54.544857009530865,
          54.69225454746054,
          54.835183549144034,
          54.98236898689759,
          55.12719972160686,
          55.270212383949016,
          55.41779180396307,
          55.5595721429318,
          55.697081292243176,
          55.83914094804922,
          55.97736523650002,
          56.111534879278764,
          56.25020498403974,
          56.38645900735883,
          56.51367827978848,
          56.64776222024372,
          56.78251438442593,
          56.909366023198594,
          57.040318993678504,
          57.17158153518691,
          57.29455922325618,
          57.41781775745749,
          57.542017283887716,
          57.65890884103764,
          57.775994080951975,
          57.894729838987416,
          58.00725661901747,
          58.116829449580685,
          58.22776725082642,
          58.335101438886184,
          58.44103590043717,
          58.545141641703005,
          58.650076352618015,
          58.75373246759643,
          58.85807811202025,
          58.96276072138144,
          59.06704747335343,
          59.17367855214936,
          59.28262777708285,
          59.392323874391046,
          59.499333882845356,
          59.60825783531494,
          59.71530206217485,
          59.819876706411286,
          59.92659593363098,
          60.02791787166093,
          60.122374329154006,
          60.217767571857614,
          60.311784964210005,
          60.39631897828489,
          60.47765047529153,
          60.56130950611345,
          60.643002314951374,
          60.71927567435813,
          60.79446933642293,
          60.872170250747125,
          60.94843642367266,
          61.01909456115377,
          61.0901889752132,
          61.1644313222098,
          61.23440900169365,
          61.301808753309,
          61.37124894988424,
          61.43205217258117,
          61.48007162806713,
          61.52087454747573,
          61.55268056257392,
          61.57033794523745,
          61.57967333535705,
          61.58123261799172,
          61.57006687229265,
          61.543951930475444,
          61.50101671375109,
          61.443577187180125,
          61.37177551007202,
          61.284344876552744,
          61.186407860721836,
          61.07364102809763,
          60.94148279358354,
          60.7947987289158,
          60.628772512865936,
          60.44807794113385,
          60.26022406482096,
          60.05428806671372,
          59.83236113594278,
          59.600819019064595,
          59.35483808704782,
          59.092657464317774,
          58.83026684654099,
          58.55672615133106,
          58.26491473000322,
          57.98173409242346,
          57.68944967785447,
          57.37211030881352,
          57.065809140174515,
          56.74713234501805,
          56.41122980633165,
          56.08215437372467,
          55.747268511748246,
          55.39019286938688,
          55.033145683768126,
          54.67964840612432,
          54.31199650127023,
          53.93933597616171,
          53.57322727179192,
          53.2088619419737,
          52.841202673940835,
          52.46752251759267,
          52.0920565467725,
          51.71929275257745,
          51.34383573646989,
          50.965414975173125,
          50.592039278483,
          50.21360665858586,
          49.82624288051308,
          49.44608107791579,
          49.073072096355226,
          48.68484008220616,
          48.31211375553175,
          47.95458871554521,
          47.58063883752528,
          47.2153466136471,
          46.867906773775225,
          46.50467714820476,
          46.149094202608886,
          45.801557912220005,
          45.44249150449991,
          45.08611015073263,
          44.73382850434776,
          44.371005246721474,
          44.00688512625639,
          43.65144174700234,
          43.28081489390871,
          42.90953975452277,
          42.54493878237917,
          42.16822904180096,
          41.79544680953694,
          41.42848455489019,
          41.0569993185093,
          40.684784571572024,
          40.311666830515044,
          39.946076102256484,
          39.57015425007888,
          39.19333837881301,
          38.82104700025099,
          38.44906853875514,
          38.07753529033888,
          37.70453294888627,
          37.33650472765199,
          36.97085062240488,
          36.602577447663975,
          36.19554793947306,
          35.836765679249915,
          35.472631217829154,
          35.10559550585509,
          34.74778256601126,
          34.38818681402771,
          34.03296686912532,
          33.68179901785343,
          33.32388162152203,
          32.97244564883373,
          32.62906622284139,
          32.27022652984324,
          31.910448589408816,
          31.57046358561761,
          31.207735566984358,
          30.840143538282717,
          30.490098702470352,
          30.13236394494525,
          29.757784668208508,
          29.407585765733774,
          29.05478277754968,
          28.684160144331962,
          28.32768425612499,
          27.980344111444065,
          27.62038291400361,
          27.265631676199437,
          26.922935248991845,
          26.57214733668604,
          26.218275301379094,
          25.86892713900485,
          25.525130751460914,
          25.17270247346353,
          24.820851901061474,
          24.479141590368958,
          24.13227361836511,
          23.784312416529406,
          23.445501267289572,
          23.11108379645721,
          22.769838631959008,
          22.42729129524143,
          22.088481558984395,
          21.7425621059889,
          21.386782669371648,
          21.037810565939633,
          20.686155558984794,
          20.32909523607062,
          19.976520951459147,
          19.61785401656065,
          19.254572972223155,
          18.892936676247537,
          18.530943889940545,
          18.162213685962982,
          17.795607207771546,
          17.43709267306614,
          17.064876487452445,
          16.69286255937941,
          16.323836228081472,
          15.93439991314548,
          15.550624617509252,
          15.169587009951547,
          14.777798962571978,
          14.39327652990857,
          14.010164666176923,
          13.620053313641371,
          13.240472869863268,
          12.855649660386884,
          12.457656460717581,
          12.087309596379711,
          11.709082269627443,
          11.305617505125515,
          10.930042676161868,
          10.552853859191243,
          10.153555819327073,
          9.765876715173547,
          9.385816477220772,
          8.98506470516248,
          8.600912941591435,
          8.2472130090847,
          7.883430395603922,
          7.523330710997504,
          7.174807110242863,
          6.818133961648295,
          6.458287936440017,
          6.1055557477686495,
          5.744899707929617,
          5.384899242974408,
          5.016762180625916,
          4.639514089040035,
          4.259448767562861,
          3.8799250689214406,
          3.5066850650037455,
          3.130571960102859,
          2.7545390538483923,
          2.381519482004951,
          2.011549784417578,
          1.636819093126453,
          1.2627461484560363,
          0.8899167223419955,
          0.5149138488284759,
          0.13951066804923412,
          -0.2296033268271061,
          -0.591829481554159,
          -0.9573890043522815,
          -1.3166312642264035,
          -1.6669610420107002,
          -2.0145518803280438,
          -2.358203833896228,
          -2.692206333792402,
          -3.0249828635782507,
          -3.3557618429030107,
          -3.6816599275330524,
          -4.016322961691832,
          -4.351571897100986,
          -4.675807072225649,
          -5.041576474438306,
          -5.378514314993975,
          -5.7039036488851185,
          -6.02861948480421,
          -6.358260529889325,
          -6.676209376700972,
          -6.989398990788357,
          -7.312298479580842,
          -7.6236194742443555,
          -7.927205615455769,
          -8.240102947187161,
          -8.543009513448073,
          -8.838444679863796,
          -9.137091857448395,
          -9.415722084809714,
          -9.691691680682883,
          -9.965773486513827,
          -10.218589818676252,
          -10.465514082027534,
          -10.712818963107472,
          -10.944972752958886,
          -11.173853063918022,
          -11.402659063638243,
          -11.626426552006645,
          -11.851278530386587,
          -12.066220910704354,
          -12.265764676120943,
          -12.45828065849491,
          -12.63974964329277,
          -12.812596511472101,
          -12.964719668410408,
          -13.095294771471865,
          -13.214339362907191,
          -13.309465808223615,
          -13.381200570507621,
          -13.440495933906309,
          -13.48485224290256,
          -13.509996579861,
          -13.515912248322786,
          -13.500791456951184,
          -13.464092162041537,
          -13.406465305272217,
          -13.330448626995928,
          -13.236713126610788,
          -13.121820887101268,
          -12.988946983863665,
          -12.839521300856248,
          -12.670847189035445,
          -12.486159298049978,
          -12.26964340203116,
          -12.05784575956907,
          -11.830414994001524,
          -11.593130857039451,
          -11.343976837364954,
          -11.081427559928919,
          -10.811469593127093,
          -10.535280039116042,
          -10.249323704083963,
          -9.959281481145865,
          -9.663436591566693,
          -9.359519135571645,
          -9.055676396199996,
          -8.746249492785685,
          -8.426506664897529,
          -8.107769917340214,
          -7.789079683603949,
          -7.43187617424925,
          -7.106811805114043,
          -6.781308953675875,
          -6.457427865651798,
          -6.135067137444237,
          -5.8076078210946935,
          -5.485660342494167,
          -5.163982711028811,
          -4.842804830095412,
          -4.525497963425851,
          -4.202286730925984,
          -3.8872365048945516,
          -3.5710007459511868,
          -3.2493033790092642,
          -2.9307718569842347,
          -2.622909204046957,
          -2.311799986789748,
          -1.9929130432471385,
          -1.6879130536560099,
          -1.3801645624367718,
          -1.0786901109785534,
          -0.7705709269465955,
          -0.45871066379595865,
          -0.16591942495330286,
          0.13388850852863304,
          0.4386527176271459,
          0.7271016700638674,
          1.0147017642829126,
          1.312925412256923,
          1.599547572556182,
          1.875647084564698,
          2.1607866979288173,
          2.4405236677390967,
          2.7088855627183834,
          2.9821984624413624,
          3.2807639018105226,
          3.544126139165194,
          3.8052634940311676,
          4.066878661153095,
          4.327566222075714,
          4.586850509581693,
          4.84374354429191,
          5.102617470320565,
          5.361612688753339,
          5.620601378978854,
          5.882371534952736,
          6.144447683011872,
          6.408028410118787,
          6.670309283992486,
          6.93518484682412,
          7.199380948441766,
          7.4592094822253205,
          7.720781631205502,
          7.984802436534399,
          8.241033501825141,
          8.495310167576601,
          8.756498462701014,
          9.01279369066786,
          9.267185207063543,
          9.524648071103888,
          9.778804858863614,
          10.032278542536712,
          10.286735654355022,
          10.545834201612884,
          10.808438749298523,
          11.065849071428358,
          11.329283903918698,
          11.599905800962043,
          11.869236803334779,
          12.14395574068719,
          12.422198556594,
          12.694262219069953,
          12.973886411152089,
          13.261834923721766,
          13.544937046851691,
          13.835374000449056,
          14.137318148082358,
          14.44031304259292,
          14.750956372342285,
          15.072998599781041,
          15.396776005795898,
          15.725591150462137,
          16.05812728995256,
          16.401111259621587,
          16.743713804636872,
          17.08569379124639,
          17.43713552016897,
          17.79009196415209,
          18.137325966390065,
          18.485598410218454,
          18.841061012833208,
          19.1947311733276,
          19.55024998889843,
          19.91739273560585,
          20.279800851750586,
          20.641698825072954,
          21.01626753275855,
          21.381437269980324,
          21.74945836364647,
          22.123307300275794,
          22.49810250771896,
          22.873446513383893,
          23.25454720162248,
          23.633985364458233,
          24.017236684911364,
          24.400465324202926,
          24.780432533521612,
          25.165300920798973,
          25.553796097726693,
          25.94090905050499,
          26.329928742885684,
          26.72625019593362,
          27.127724848900797,
          27.524905111658466,
          27.919932337766923,
          28.32272714539061,
          28.721867424026556,
          29.10499095204518,
          29.501284213662537,
          29.902546573077874,
          30.289747900845505,
          30.687852056436082,
          31.096502013698338,
          31.498374388560404,
          31.89864995764112,
          32.31440908050786,
          32.72648830702518,
          33.12853595823151,
          33.547462960297494,
          33.96920776536035,
          34.37413899475233,
          34.7848389750732,
          35.2014649572255,
          35.597268719613716,
          35.99926741469605,
          36.408458444436256,
          36.80721240488395,
          37.20257949248309,
          37.60052453329765,
          37.991657355594654,
          38.373106260558764,
          38.7586474969034,
          39.15054874965966,
          39.531146311052645,
          39.91638877380719,
          40.3052011809927,
          40.67213221278191,
          41.031639581896655,
          41.38904008884563,
          41.740934311828376,
          42.068906969612975,
          42.403283573499834,
          42.739995148320155,
          43.05545313539726,
          43.374885587472235,
          43.69105050585382,
          44.034718590261754,
          44.399440405877925,
          44.75573882919998,
          45.11269320822648,
          45.47207171954012,
          45.82321291832529,
          46.167324051461485,
          46.529838813112896,
          46.867935361514974,
          47.20358920137738,
          47.53154596324945,
          47.82824565864461,
          48.13035638881362,
          48.439578661092845,
          48.72878415650247,
          49.01799174590698,
          49.31509378649518,
          49.59065565637017,
          49.872446879664224,
          50.161030673020164,
          50.43093707360798,
          50.71653099600174,
          51.00801499391844,
          51.28412378986799,
          51.570232325542904,
          51.84684824699016,
          52.10135537498573,
          52.36382541889213,
          52.62285233340489,
          52.857304296666236,
          53.08168246480826,
          53.297658560875924,
          53.494553520301,
          53.682882360170154,
          53.86564705686268,
          54.03316019127849,
          54.18906611239944,
          54.335096088576485,
          54.47040493086842,
          54.5981560552488,
          54.71558719964669,
          54.820270750345635,
          54.91759047027468,
          55.01055491161814,
          55.09588636158094,
          55.17623508168371,
          55.252569539690406,
          55.32559478133029,
          55.39501599037662,
          55.45728538600888,
          55.51160645854966,
          55.56203731730469,
          55.60777989868791,
          55.6497247389787,
          55.68871194470887,
          55.72431214489305,
          55.75557230577191,
          55.78536217914103,
          55.81369211386821,
          55.840490438198856,
          55.86707253324583,
          55.89317166298818,
          55.917497181025844,
          55.938754360869986,
          55.9578805013551,
          55.975057160104434,
          55.99200341947563,
          56.008960749704706,
          56.02611811151575,
          56.04551855081822,
          56.065612828790556,
          56.08624290434219,
          56.10849143838573,
          56.13327154137771,
          56.15864056253118,
          56.18625727930865,
          56.21526082904195,
          56.24609847812245,
          56.27941913145412,
          56.31335090786335,
          56.34825342646937,
          56.38488166382764,
          56.422272186809735,
          56.45978262271737,
          56.498774051881874,
          56.53963479954145,
          56.58270614033862,
          56.62631234549384,
          56.666835504765636,
          56.70561396556938,
          56.74447719423239,
          56.77953562869674,
          56.81235956700406,
          56.84522458717532,
          56.874152619023114,
          56.89958071593323,
          56.92362663322244,
          56.94608380077201,
          56.96512763148799,
          56.9810790312063,
          56.99099649348849,
          56.99733998415812,
          57.001302773784445,
          57.002257291044984,
          57.00164993548657,
          56.99998009121031,
          56.99684186251042,
          56.99268569402752,
          56.98721195516007,
          56.97963365895441,
          56.968764749230175,
          56.95480109752451,
          56.941476203504855,
          56.926593043316956,
          56.90965162175531,
          56.89141894751151,
          56.872775902199436,
          56.852442614849934,
          56.83026612892718,
          56.807155095724006,
          56.78434553057613,
          56.762774392814606,
          56.74061184045273,
          56.71773567127197,
          56.694092432452265,
          56.668751995777875,
          56.64301787073612,
          56.61360022029209,
          56.58706620967639,
          56.56200859435146,
          56.535993205281834,
          56.50908694382358,
          56.483003094332055,
          56.45838257856404,
          56.4346862193037,
          56.40936271856511,
          56.385699750130506,
          56.36241765049165,
          56.33407824649129,
          56.300186924489005,
          56.2626047742628,
          56.217622540906355,
          56.164301967674,
          56.104470415148654,
          56.03568400588743,
          55.958923235646004,
          55.87017771658777,
          55.771115929307356,
          55.66050217532969,
          55.53044770724891,
          55.38055949319694,
          55.216001877033484,
          55.03403979101949,
          54.839375040529994,
          54.62895565047312,
          54.40213511838124,
          54.162324164496454,
          53.90124285846883,
          53.622444319674706,
          53.3366974726652,
          53.07248271198428,
          52.79705010867054,
          52.507318094547344,
          52.21294697273232,
          51.92120120248295,
          51.61207252562718,
          51.30699332943816,
          51.00734363108432,
          50.702721721217024,
          50.38718403716465,
          50.04851660808337,
          49.707037104368034,
          49.360224670300354,
          49.00487502463951,
          48.641829306869624,
          48.278330910604694,
          47.90812569109004,
          47.53010797359777,
          47.14905486851263,
          46.77431686372914,
          46.39850932456343,
          46.01506796786698,
          45.649455406700426,
          45.28012244268648,
          44.90598094101536,
          44.54835840428026,
          44.19305491361802,
          43.831669333156846,
          43.481563082465144,
          43.130917728424755,
          42.77102309335774,
          42.42588471985768,
          42.088970847074165,
          41.73601757904162,
          41.4070432000424,
          41.09028077060689,
          40.75586405661557,
          40.43920184656599,
          40.13908606542127,
          39.820912095716515,
          39.51821026570658,
          39.22565784053581,
          38.92544930996288,
          38.62890237091544,
          38.33675220193973,
          38.04031603291111,
          37.74089227426836,
          37.4523878475412,
          37.15338460713522,
          36.84949927002007,
          36.547048751106004,
          36.240560246554416,
          35.929161909053114,
          35.62311824272138,
          35.3183424998264,
          35.01037187522542,
          34.707709613049104,
          34.39915913979863,
          34.099861708615606,
          33.79279965725131,
          33.487875124784374,
          33.183087723674696,
          32.87830187627792,
          32.577227629946606,
          32.27096875349995,
          31.965519217591762,
          31.66172759978884,
          31.354365384492315,
          31.046656141832095,
          30.738625668025836,
          30.43607848762624,
          30.12677037888246,
          29.81739633486835,
          29.51947034584702,
          29.218203390804486,
          28.92149718800499,
          28.63320082420781,
          28.342611341872676,
          28.056307698892773,
          27.778988845446865,
          27.496641777074625,
          27.203736782492673,
          26.928179703117003,
          26.654071999193174,
          26.360346835877365,
          26.08156308849356,
          25.8090037438668,
          25.525486766014126,
          25.24645351763025,
          24.978613261245844,
          24.707167086692618,
          24.430153252330985,
          24.161261099425584,
          23.890192597742644,
          23.619054792305313,
          23.34488060380485,
          23.07430620809438,
          22.801931440354025,
          22.525441500138093,
          22.244284613603494,
          21.965360344997897,
          21.68341061143713,
          21.389656174831394,
          21.10467362856162,
          20.82047946996094,
          20.53505359737702,
          20.245510637256043,
          19.967293857664238,
          19.691222198091676,
          19.411483917414408,
          19.138347021124353,
          18.864962985798453,
          18.589269426263186,
          18.31100174176081,
          18.03492111190702,
          17.75558296647682,
          17.473562671069693,
          17.200438934518257,
          16.917401201824916,
          16.631651987269017,
          16.359695686680062,
          16.083964508251945,
          15.808445329769434,
          15.528998344664615,
          15.246312974770017,
          14.963048683336664,
          14.678183598668438,
          14.38567804772808,
          14.09108602102483,
          13.79067820563298,
          13.484981238648714,
          13.17233610697443,
          12.854409475124706,
          12.543579069186688,
          12.224576288312015,
          11.903988117926017,
          11.590515042156978,
          11.27156361328683,
          10.937149255696873,
          10.621284336546001,
          10.307138076044264,
          9.96187736183818,
          9.633799869322353,
          9.316861496514987,
          8.975615959095764,
          8.640931975238832,
          8.314022543478073,
          7.976308910818991,
          7.636775708274165,
          7.304373279250715,
          6.966748681866484,
          6.626228722662883,
          6.290696473460649,
          5.94855215362453,
          5.606647634962997,
          5.262264275062881,
          4.915850589696338,
          4.56503725971969,
          4.215819886913209,
          3.862648417740447,
          3.5067342928165557,
          3.1521366230353665,
          2.7905079156473334,
          2.4331973674042784,
          2.0733013157448377,
          1.7096896004210587,
          1.3468153360950268,
          0.9843736049861767,
          0.6206651559982981,
          0.25386579255841035,
          -0.10787248571359065,
          -0.4647305094568017,
          -0.8277431577087507,
          -1.188716416606794,
          -1.5396355120916694,
          -1.8932530120750826,
          -2.2583644158023266,
          -2.603560017956953,
          -2.94857786189462,
          -3.299685367007091,
          -3.641631300058217,
          -3.9777075859163875,
          -4.311540341567952,
          -4.647905601911665,
          -4.98643944564314,
          -5.3161867597026315,
          -5.645378308979822,
          -5.982064220250516,
          -6.309198909992838,
          -6.625696462397852,
          -6.959890518684558,
          -7.279114416760989,
          -7.5801872903702785,
          -7.898283006223394,
          -8.215782352106562,
          -8.511581200654915,
          -8.81823986077847,
          -9.117396045045018,
          -9.40529871691725,
          -9.703334169787272,
          -9.968453923865091,
          -10.227751449352153,
          -10.49488408352675,
          -10.737110431797747,
          -10.964925381875702,
          -11.192439612456948,
          -11.401710433912035,
          -11.597219541926718,
          -11.78649369066499,
          -11.960974289084511,
          -12.121558477089204,
          -12.274004597117614,
          -12.414278156546354,
          -12.539394400219807,
          -12.651796775165819,
          -12.750172513848746,
          -12.833263999671926,
          -12.898343621041262,
          -12.944115314510055,
          -12.970450817396848,
          -12.975166246931376,
          -12.957854522222375,
          -12.915919799690897,
          -12.851487504768736,
          -12.766147034397553,
          -12.657835511816371,
          -12.529562243907494,
          -12.382168859257977,
          -12.212984734604289,
          -12.022222884524053,
          -11.813070345141318,
          -11.589851849627294,
          -11.344780693265411,
          -11.082835235302445,
          -10.807150355459857,
          -10.515798799134334,
          -10.21669837731114,
          -9.912289205662937,
          -9.594714083095585,
          -9.268121412855555,
          -8.938893856842977,
          -8.599022533715896,
          -8.218035145122501,
          -7.872654199631793,
          -7.521511439317353,
          -7.169695461721039,
          -6.817039824455227,
          -6.462762387535386,
          -6.113915135750591,
          -5.7617602594028465,
          -5.409145548072722,
          -5.059375207302049,
          -4.7073067158858874,
          -4.355453720158067,
          -4.004345884288577,
          -3.6555353066442637,
          -3.306697587703429,
          -2.9549071260976794,
          -2.6056834721656603,
          -2.2547126947573575,
          -1.016144631818952,
          -0.6593447068545467,
          -0.29691349244891246,
          0.06682109086171656,
          0.42267325086137597,
          0.7813629011494736,
          1.1464116872567325,
          1.4985278040133412,
          1.847828384791398,
          2.1944482616636787,
          2.5560238488109652,
          2.9089475188257614,
          3.248541863940694,
          3.6071166754576898,
          3.9611254341968856,
          4.29951460278969,
          4.649203489040254,
          5.004768934062478,
          5.341215066110188,
          5.683026295931434,
          6.035152746299424,
          6.371613634847714,
          6.710384205710767,
          7.055907689133003,
          7.391088314122611,
          7.723706761010639,
          8.059606274998435,
          8.399822638319982,
          8.737262714589445,
          9.072764668335603,
          9.411394409922703,
          9.750168634756196,
          10.086398424812142,
          10.427871163356038,
          10.770141606423742,
          11.112137081393188,
          11.45508885312039,
          11.801456017264574,
          12.143606023859176,
          12.481942940541515,
          12.823880464472007,
          13.164568009481984,
          13.495294709750159,
          13.830083006709483,
          14.170955919684296,
          14.501566572749946,
          14.835912197727998,
          15.172442622621617,
          15.506267221802657,
          15.839129408792655,
          16.18113497915037,
          16.526883586559574,
          16.865436657362082,
          17.214431431623144,
          17.569915001443942,
          17.92107011923,
          18.27697382081262,
          18.629669892403687,
          18.974664218883955,
          19.329598141794772,
          19.683660795842304,
          20.037833166246752,
          20.406925935986468,
          20.77969883510911,
          21.155172943833268,
          21.543468568745645,
          21.933708084255827,
          22.322769562578095,
          22.71685622794749,
          23.117219972608545,
          23.506586144966622,
          23.901943228873048,
          24.302859177000435,
          24.692795543066143,
          25.078906741171313,
          25.47115779143322,
          25.862400063794517,
          26.239704017299378,
          26.6150304365897,
          26.98916615447716,
          27.3561448797532,
          27.731475046043933,
          28.132988239803222,
          28.496582464071857,
          28.864531397545658,
          29.22946662361722,
          29.593362792573764,
          29.9689814226995,
          30.347515479261563,
          30.72503102136061,
          31.106642370879552,
          31.47985463613509,
          31.851931624853773,
          32.225114075915926,
          32.59535383595824,
          32.9683166877988,
          33.34025448514065,
          33.70690669880313,
          34.06789038744542,
          34.42489888646252,
          34.78197595343813,
          35.14068119064813,
          35.49968765818269,
          35.847348483160104,
          36.19502013226061,
          36.55285549019777,
          36.903679690722576,
          37.254313549553984,
          37.62096065220641,
          37.99019885205885,
          38.354835747346755,
          38.717330858397546,
          39.08805854400857,
          39.45769299447226,
          39.820194113275996,
          40.186930864553055,
          40.55830313266503,
          40.92637271855744,
          41.29350248721418,
          41.66182453114698,
          42.02773198370218,
          42.38898935582809,
          42.743691438432414,
          43.09952598950704,
          43.45621614353036,
          43.807111789810214,
          44.15206120455052,
          44.49881874566006,
          44.84529438441963,
          45.18294435790405,
          45.51704133575203,
          45.85655652158104,
          46.19523093613297,
          46.53007774290174,
          46.86857589089276,
          47.211413736876786,
          47.54622747104714,
          47.87276187551954,
          48.19569546135149,
          48.519195885036176,
          48.84260235486342,
          49.1473908981684,
          49.46374395892525,
          49.78029019133622,
          50.08493866689776,
          50.39204986447101,
          50.69319910828734,
          50.99132840440384,
          51.29192071105291,
          51.582045384248445,
          51.872471859917276,
          52.1592504111497,
          52.4350525913333,
          52.70901959667804,
          52.98711179932178,
          53.23758650158044,
          53.49646772508539,
          53.75713529197604,
          54.002655723677016,
          54.255169822508606,
          54.49764875251168,
          54.72549938618048,
          54.95806390038172,
          55.18029935360197,
          55.38916754716942,
          55.60544845519947,
          55.80996449878175,
          56.00416256686348,
          56.20602419424737,
          56.39689791882204,
          56.5819638418341,
          56.76605931488675,
          56.93121186961011,
          57.0847437656932,
          57.24087262915049,
          57.3841441269592,
          57.50971834427297,
          57.62984755985808,
          57.7394818044663,
          57.8357333791372,
          57.92317404854355,
          58.00007169204911,
          58.06464848285505,
          58.118889449338944,
          58.16351942840969,
          58.20018761272942,
          58.22886715626672,
          58.248042460390316,
          58.256639159487,
          58.2568197075274,
          58.248665075037955,
          58.22969429536686,
          58.20419783083681,
          58.17560086311876,
          58.141548691773025,
          58.101857499033954,
          58.060145303296245,
          58.011058868062456,
          57.95489809423012,
          57.897603938181994,
          57.84009500065257,
          57.774109457229166,
          57.70487994792536,
          57.63580509237289,
          57.56282063930549,
          57.486398785431106,
          57.41099580810595,
          57.334142946106496,
          57.25537022169586,
          57.17719709774812,
          57.09592902731557,
          57.01470632604266,
          56.93447193980057,
          56.85307117702178,
          56.77029213847556,
          56.68748898081699,
          56.60171108044309,
          56.5144062955533,
          56.42697707059443,
          56.33888147756388,
          56.249912172280084,
          56.163371018533866,
          56.074755366893996,
          55.985709385729166,
          55.897674213490085,
          55.806567331121016,
          55.716551287058394,
          55.62852978140373,
          55.54110829949496,
          55.452063913251514,
          55.36928513113563,
          55.28299417322558,
          55.194485989480135,
          55.10741852876635,
          55.014959570444105,
          54.92078588489622,
          54.828211820035186,
          54.731937231042934,
          54.63481426538961,
          54.54185814289958,
          54.45039042089325,
          54.353863355020806,
          54.25830390614105,
          54.16355367013178,
          54.067183952066834,
          53.96961556322214,
          53.875489068239254,
          53.782588779146074,
          53.68728669789345,
          53.59160240253313,
          53.493813961135,
          53.39312249025475,
          53.293917428978496,
          53.19549328311058,
          53.09784616416041,
          53.00343346813311,
          52.91138524518661,
          52.816895899896316,
          52.72559033045191,
          52.63372847956242,
          52.537673534742126,
          52.438352767813484,
          52.335850437803785,
          52.23429022460171,
          52.13032291459659,
          52.02138747127137,
          51.9091621323457,
          51.7955864664183,
          51.68045543786064,
          51.56484038437353,
          51.449693409955174,
          51.333268513282285,
          51.22080427580808,
          51.11119085894538,
          50.998876538331565,
          50.884358210639235,
          50.76843972732959,
          50.6547493701092,
          50.53670168027883,
          50.414539489854974,
          50.29250382161416,
          50.16923226197554,
          50.04648686772441,
          49.915343279841046,
          49.78405666415551,
          49.6547537874927,
          49.5227238004472,
          49.382419832792245,
          49.24782791651712,
          49.1139395589107,
          48.96570417039539,
          48.813339413030064,
          48.66321947995453,
          48.50128959409817,
          48.32829467363929,
          48.163317734267125,
          47.99783935450026,
          47.811215670249794,
          47.615792104090346,
          47.42010955719554,
          47.202104508530084,
          46.97541122544629,
          46.74832788648891,
          46.503515383730296,
          46.257124492157836,
          46.00443966411958,
          45.737693166825295,
          45.466144122088366,
          45.18918840755828,
          44.896555531244026,
          44.60083749977606,
          44.30263169740128,
          43.98121558449072,
          43.65122579502918,
          43.320550280330075,
          42.97924154608048,
          42.62774551219158,
          42.27931734017526,
          41.930926612424564,
          41.57160453423903,
          41.22628263456777,
          40.88772771176841,
          40.53334759994677,
          40.18087262972471,
          39.84929522337897,
          39.50183422096595,
          39.15547316248579,
          38.82199146021086,
          38.48419826495861,
          38.13588746646588,
          37.7985795891807,
          37.465327585095864,
          37.12438785272797,
          36.78748070236091,
          36.460936828741694,
          36.13849174292853,
          35.818019446615295,
          35.50032179179734,
          35.19408740014488,
          34.89625721624557,
          34.602307171649095,
          34.309653977381,
          34.02623414673576,
          33.74330974570317,
          33.46000908308997,
          33.1857097589885,
          32.9177196606458,
          32.64263546308539,
          32.380992591960194,
          32.130901719529504,
          31.87157752205381,
          31.61917304560049,
          31.37988264498719,
          31.13101326647757,
          30.884323106330893,
          30.646533440124994,
          30.40408282964225,
          30.146959891245604,
          29.88448504438357,
          29.61865810262047,
          29.348917852009006,
          29.087264615127534,
          28.819257770215366,
          28.545539879660744,
          28.275144151039928,
          28.004524754651715,
          27.729003807976547,
          27.47098481153848,
          27.223162800229783,
          26.972923554608013,
          26.72677387454312,
          26.47887433409944,
          26.236261017013035,
          25.987254879866487,
          25.73616714567915,
          25.486351945808043,
          25.23541638191824,
          24.976612733565506,
          24.708836813349716,
          24.444242088522454,
          24.183680460309283,
          23.92023230755656,
          23.662138150480853,
          23.40775737023184,
          23.160553351897548,
          22.908975463679933,
          22.661340123032478,
          22.43080775202382,
          22.20553687882793,
          21.9860609892867,
          21.770918182486945,
          21.555406605446567,
          21.34986405403206,
          21.15032088740068,
          20.94772370812601,
          20.746033767161908,
          20.557948720122173,
          20.37911246069998,
          20.2050970463388,
          20.045346731317927,
          19.887660113538683,
          19.723106650941904,
          19.567161955808007,
          19.41781667897727,
          19.25912313221167,
          19.1018936338632,
          18.94802132826251,
          18.780077784699476,
          18.604879785384224,
          18.426844352999904,
          18.25017374463643,
          18.07334494052737,
          17.893627294245118,
          17.711399994261882,
          17.534140096189052,
          17.358126432405346,
          17.171053903579285,
          16.994746910297717,
          16.825380401154792,
          16.654548016098808,
          16.481239113968705,
          16.31238100766003,
          16.14682618402819,
          15.976957195972991,
          15.807003608531945,
          15.63030631280838,
          15.448823938741326,
          15.256503734705,
          15.055776462028861,
          14.853561737107857,
          14.642350626253576,
          14.42957160162266,
          14.216913929764194,
          13.99637284496533,
          13.772255968871258,
          13.543923645364524,
          13.310583581208467,
          13.081051851545233,
          12.842513876182316,
          12.600887179171432,
          12.365494317937173,
          12.125053940886609,
          11.87754675994134,
          11.634779045426287,
          11.391636950288863,
          11.138752588746124,
          10.885737495057397,
          10.637110817193527,
          10.37631275176222,
          10.120747349680473,
          9.866323904194086,
          9.603697820146095,
          9.332286823133868,
          9.0748035923133,
          8.814631046542207,
          8.530801654482412,
          8.26847597313656,
          7.998613394407122,
          7.709034026499522,
          7.426737459710137,
          7.145135392698271,
          6.855922882173727,
          6.565047225511663,
          6.2805755454440995,
          5.990557694676198,
          5.699136396613642,
          5.410124824571167,
          5.120077302615389,
          4.831230677099671,
          4.54207279813495,
          4.252944707874897,
          3.9586098010546507,
          3.669764536832375,
          3.3765471139175487,
          3.0878020454357307,
          2.800668191323897,
          2.509544658820502,
          2.2238096768409816,
          1.9397069578386525,
          1.6500897063979356,
          1.362347080419284,
          1.0772277250530258,
          0.7910930729576051,
          0.5020353633970458,
          0.21958796629526706,
          -0.060293937664332276,
          -0.34665879499137725,
          -0.6310382034723865,
          -0.9060391670727266,
          -1.1798149642421087,
          -1.4612438091295152,
          -1.7260298304563348,
          -1.9870151144306107,
          -2.255890685863474,
          -2.51332495304702,
          -2.7681952879705367,
          -3.025491755782631,
          -3.2823477372675747,
          -3.5414708569113142,
          -3.803992522585109,
          -4.0609974068591885,
          -4.323129468016861,
          -4.584471712017325,
          -4.836342448098703,
          -5.099679855212179,
          -5.352847808689377,
          -5.5982512165993565,
          -5.848306335182828,
          -6.09036860514888,
          -6.322384989945734,
          -6.550318190646657,
          -6.774286712598426,
          -6.988667685569313,
          -7.199921601710623,
          -7.399068101227516,
          -7.588067265110479,
          -7.774274646162148,
          -7.948121765275557,
          -8.111447390893122,
          -8.269613069632488,
          -8.41651431549843,
          -8.55200273365739,
          -8.67634862753494,
          -8.78987639016042,
          -8.89117457887087,
          -8.979672196526547,
          -9.053647673504077,
          -9.111662863150716,
          -9.153118241515317,
          -9.177439947421492,
          -9.182679654991453,
          -9.164435525480405,
          -9.122535578493585,
          -9.059180953482048,
          -8.966721078634922,
          -8.84719695506742,
          -8.709832818046813,
          -8.546924630265831,
          -8.363554638520565,
          -8.164954223425692,
          -7.945885542441818,
          -7.707600011315168,
          -7.45303802312471,
          -7.187178875430662,
          -6.904081494774582,
          -6.607476668832274,
          -6.302587949724487,
          -5.985350965623969,
          -5.666028423818949,
          -5.344198943377727,
          -5.015818853909928,
          -4.682784448086348,
          -4.351447614988249,
          -4.01687874605739,
          -3.6809000214827328,
          -3.345357551805807,
          -3.008512821048182,
          -2.673979506163399,
          -2.3397883323658,
          -2.0053681283661695,
          -1.6771229294828973,
          -1.3459446271774362,
          -1.0144560215997926,
          -0.6882772597742572,
          -0.3597937308891938,
          -0.028713806931663866,
          0.3009334585075025,
          0.6288209474265939,
          0.9906581931130227,
          1.3229981073005046,
          1.6528271932735743,
          1.9834804546204001,
          2.3158101796974684,
          2.650389499645336,
          2.989698323975892,
          3.3303782701733358,
          3.67362537437298,
          4.0256435901686025,
          4.377563864505549,
          4.726978463147397,
          5.088270473534252,
          5.446698852249907,
          5.805426737360769,
          6.162648068491221,
          6.537312796135578,
          6.906323029752279,
          7.264904769651772,
          7.648205452805329,
          8.028705949725971,
          8.39481433418138,
          8.775486502453115,
          9.164022319070252,
          9.534991230269316,
          9.91797625104327,
          10.307106815210924,
          10.681830130858234,
          11.064319217170734,
          11.449135985864679,
          11.822286885609556,
          12.197967429029495,
          12.583588751817393,
          12.963715083103914,
          13.339447140418724,
          13.72308593987491,
          14.10818544495083,
          14.487205736668509,
          14.872303321247559,
          15.264265386621576,
          15.654693611545001,
          16.045843922128682,
          16.44264593510048,
          16.832226639154566,
          17.21709171809061,
          17.607646634318066,
          17.98703884753735,
          18.360256176383263,
          18.745020681817333,
          19.122283620366723,
          19.494047547673123,
          19.871883338024883,
          20.25025525227716,
          20.620143493119027,
          20.996648415891052,
          21.379095723299685,
          21.75120988024822,
          22.128902431355506,
          22.549028405390022,
          22.92257552152903,
          23.298492799534674,
          23.668039618765476,
          24.034418180630414,
          24.402587775607156,
          24.768509258560105,
          25.14092822366267,
          25.520675120181387,
          25.89587035681767,
          26.281559208811142,
          26.67579382364871,
          27.06094841140931,
          27.443116739652332,
          27.836726486238437,
          28.220730891261532,
          28.598404621714625,
          28.986670185687952,
          29.368667031179605,
          29.735330368782186,
          30.10698685884798,
          30.488333490875757,
          30.85604320241579,
          31.231458714020444,
          31.610428430291396,
          31.981387603217183,
          32.35147615571863,
          32.725201401803595,
          33.090163939738815,
          33.45714896101673,
          33.82373504984475,
          34.190023025847744,
          34.55467782749827,
          34.91993996208546,
          35.28209442854368,
          35.64771721796965,
          36.00808404331896,
          36.363754253246114,
          36.72175203849156,
          37.0766317342795,
          37.43179336496569,
          37.787541168055846,
          38.14628469754537,
          38.505612032640514,
          38.86385894889629,
          39.22160109609035,
          39.58281340265719,
          39.942272359667086,
          40.2909610335045,
          40.6467467456102,
          41.00943179588437,
          41.39339467250685,
          41.745327077367385,
          42.10756385294624,
          42.46416835450666,
          42.813080626938905,
          43.17076516555194,
          43.530657740696626,
          43.88048509542785,
          44.23209581492437,
          44.58887016261397,
          44.93822925178907,
          45.28542915062545,
          45.63212764383536,
          45.976375664207836,
          46.31569444536887,
          46.64991857063094,
          46.98564606356336,
          47.321883982566234,
          47.64909307566419,
          47.9751049527662,
          48.34048032252985,
          48.66693411421494,
          48.985844207941184,
          49.3108016268647,
          49.63670035314136,
          49.9593325086482,
          50.28244189043483,
          50.60929008070905,
          50.928695093063304,
          51.23992569710519,
          51.543961489579914,
          51.85075025401761,
          52.14936616276105,
          52.43408692711314,
          52.72808444983445,
          53.01386257315126,
          53.29189700453342,
          53.566049763412636,
          53.833545106028154,
          54.09520349323003,
          54.37086918180053,
          54.63662494331925,
          54.89861891143578,
          55.15205340272464,
          55.39346628788784,
          55.6361666685264,
          55.85404262031117,
          56.073175974680794,
          56.290664268951645,
          56.493493350033795,
          56.682564783040604,
          56.859825735682755,
          57.02611248973415,
          57.19278327516731,
          57.34786474456324,
          57.49352738841198,
          57.64208441539389,
          57.77824828335502,
          57.90325866739047,
          58.026066272551375,
          58.13497327538347,
          58.23738653231144,
          58.33204417169462,
          58.410107921082485,
          58.47934173556328,
          58.545108023930155,
          58.59728381719211,
          58.63235198478038,
          58.65698705479223,
          58.67059514290284,
          58.67287685816191,
          58.66331579414038,
          58.641028586388636,
          58.60497545332039,
          58.554691873595644,
          58.49210613343218,
          58.41795591290818,
          58.33025605033609,
          58.233244842556886,
          58.1289313021224,
          58.00953886144346,
          57.8847753613733,
          57.755545790777425,
          57.62198379887005,
          57.489626431310825,
          57.3545590289746,
          57.21034560762268,
          57.06810764394721,
          56.924392466209,
          56.77141156498824,
          56.618519142870355,
          56.46650087897269,
          56.312699591565114,
          56.14783236248102,
          55.98127169651004,
          55.81325362599921,
          55.640681113484476,
          55.463359867676985,
          55.28486447754226,
          55.10360758017922,
          54.92062582233616,
          54.737989991586964,
          54.551390604301346,
          54.364011487690796,
          54.178580706612046,
          53.990632158596966,
          53.80028055044182,
          53.609742480587116,
          53.41514836203741,
          53.21727608030595,
          53.018675490599364,
          52.818713805094134,
          52.616883089988555,
          52.397905667915005,
          52.196155179863446,
          51.99639774843956,
          51.799775949009806,
          51.600953721753065,
          51.40861947716391,
          51.22333370824064,
          51.0374712372325,
          50.855005057686355,
          50.688353478211674,
          50.51723710675954,
          50.3455432861825,
          50.18420966713949,
          50.014774032471976,
          49.84001643121023,
          49.67033723345798,
          49.49521791401003,
          49.31761842796205,
          49.139475273930294,
          48.95933033664392,
          48.78201883995827,
          48.60116010014866,
          48.41164010110454,
          48.22460340804343,
          48.03657447342987,
          47.8409772761511,
          47.64541445104406,
          47.452407790689605,
          47.252335229036255,
          47.0488862075855,
          46.84674289594181,
          46.63773838425997,
          46.42499982516288,
          46.2182392115676,
          46.01085050903486,
          45.8043570241303,
          45.605832838573946,
          45.40521264084731,
          45.20693185152201,
          45.010951940781084,
          44.810024484071626,
          44.60403119177929,
          44.394837331665336,
          44.18681003464203,
          43.97336916175396,
          43.752453457310786,
          43.52824975368074,
          43.30260856699138,
          43.07399057832258,
          42.84597649759885,
          42.618286310099975,
          42.39456679747721,
          42.17734075859258,
          41.95813335150637,
          41.736125474207135,
          41.51449057201843,
          41.298491646435735,
          41.07445834605348,
          40.845753658880696,
          40.620731123992435,
          40.397990705663894,
          40.167896103367454,
          39.93193243618115,
          39.705918339212104,
          39.48686327720169,
          39.25550186563384,
          39.03039582169425,
          38.82213733268875,
          38.59952219886444,
          38.36562859500524,
          38.140918113165704,
          37.914551919383136,
          37.67704500904111,
          37.4327648269679,
          37.19576843222316,
          36.96346024087171,
          36.71256033806325,
          36.45569824698664,
          36.204202526053386,
          35.93594137111388,
          35.65439732910691,
          35.375069343554244,
          35.080647498042644,
          34.78159124444144,
          34.48432259043408,
          34.17601416112367,
          33.85730585675768,
          33.54022467148753,
          33.21398289048241,
          32.88057173567504,
          32.5593991025957,
          32.224338959321855,
          31.87265507606582,
          31.52941986245883,
          31.185321588093913,
          30.83495790527638,
          30.483176710360837,
          30.13984230595454,
          29.796797585259508,
          29.452398249545908,
          29.1322259691733,
          28.81259330422633,
          28.482039901889774,
          28.17419431590544,
          27.874902248263705,
          27.563809951539003,
          27.269759329242813,
          26.983040244336255,
          26.696945727645215,
          26.414159339864348,
          26.14317399628155,
          25.877638291023967,
          25.61564585304183,
          25.364128917046393,
          25.119938752473665,
          24.88640618896987,
          24.65859446559463,
          24.433826356383783,
          24.21643080004734,
          24.008157091077344,
          23.80333956225134,
          23.600609285363234,
          23.4076440355656,
          23.216191374205522,
          23.023618396041325,
          22.838021091596005,
          22.66020368462961,
          22.485041918917382,
          22.316591084404195,
          22.15788052741282,
          21.997984346471842,
          21.83896013348688,
          21.690936198905295,
          21.542541913930926,
          21.39239283017581,
          21.250398569419726,
          21.107269455421736,
          20.960765028847213,
          20.818883520396817,
          20.674993319240766,
          20.529411838200115,
          20.386071380537,
          20.242313367399,
          20.093573492457427,
          19.945424843322208,
          19.7989882397102,
          19.647953509156423,
          19.501039537502717,
          19.3556920737729,
          19.209085238573966,
          19.06330342794033,
          18.918478256689006,
          18.77486174515046,
          18.633719742302276,
          18.49000570181859,
          18.348067580210355,
          18.20713156423599,
          18.0656706274686,
          17.92719991485461,
          17.78930854430543,
          17.653967240576634,
          17.51903243840091,
          17.385085715720912,
          17.25147021804598,
          17.121157525230412,
          16.98185303784235,
          16.855799462632948,
          16.737402931218128,
          16.622222900466735,
          16.508102186416515,
          16.3973683401855,
          16.287392703540053,
          16.17888974795789,
          16.077843114009983,
          15.978509781379111,
          15.878763835543987,
          15.779724745055054,
          15.683413642691823,
          15.58394893642623,
          15.480133015069253,
          15.38560077921869,
          15.294942582353142,
          15.202954767045279,
          15.11395564612569,
          15.031383348761619,
          14.948242149173982,
          14.862989452871833,
          14.784488079339466,
          14.707975202758927,
          14.634557299443852,
          14.561178330444479,
          14.486456195534181,
          14.41355166338427,
          14.340906341707845,
          14.26773474513965,
          14.196080415019612,
          14.126438836301809,
          14.052929287433628,
          13.976312358939373,
          13.905125482021152,
          13.833979933989347,
          13.763800127267915,
          13.693954097686055,
          13.626452561139033,
          13.561447246186475,
          13.496182939018363,
          13.431471462656013,
          13.364576785567673,
          13.29585001214357,
          13.226417469600339,
          13.154359280208228,
          13.080463713908975,
          13.004086915134017,
          12.924146264629002,
          12.845026846044929,
          12.76354742233718,
          12.675264175570048,
          12.584875501159399,
          12.490826933505096,
          12.389457866110359,
          12.2833232450772,
          12.169568542283086,
          12.051591662224784,
          11.927632691096996,
          11.797434316577835,
          11.661087415284696,
          11.51508876505498,
          11.363401749670194,
          11.208025391217001,
          11.042703546607404,
          10.870557113075433,
          10.698461611548485,
          10.515109654234719,
          10.328454685155128,
          10.145049098202099,
          9.94897754958753,
          9.75200451071638,
          9.565967845310452,
          9.367609930019624,
          9.163689649461205,
          8.970504288197038,
          8.770406357156276,
          8.56133768651176,
          8.358837965309284,
          8.155067030621748,
          7.940836112770166,
          7.731509062739313,
          7.5234482583928095,
          7.28526067276694,
          7.070014317418713,
          6.854367070369595,
          6.633388634553658,
          6.410954627601904,
          6.192049275553677,
          5.9705046702960685,
          5.755387213196163,
          5.540641501117966,
          5.325883354987782,
          5.113387960963603,
          4.904037823469608,
          4.698568365125043,
          4.494646583619932,
          4.29218571797638,
          4.093804735683565,
          3.896581582931915,
          3.6993393982423237,
          3.505321696459772,
          3.3167939247334557,
          3.1278995747289886,
          2.939826740939026,
          2.752114055376342,
          2.564092687476761,
          2.375925355461953,
          2.188564650280692,
          2.0038153122997704,
          1.8179548653111994,
          1.636489682623588,
          1.4562968534847012,
          1.2772114130502996,
          1.0984468883964866,
          0.9185990675512066,
          0.7422600774377751,
          0.5654532985069779,
          0.3878533244882312,
          0.21078542518007173,
          0.037122848075738596,
          -0.13821766985363051,
          -0.30730480925290515,
          -0.4669344715889308,
          -0.629604770435598,
          -0.7979579967315752,
          -0.9616886513649983,
          -1.1202269848165958,
          -1.2842019743708855,
          -1.441649735100221,
          -1.5919414639715663,
          -1.7476787980126764,
          -1.897477187769446,
          -2.0350045674053407,
          -2.1697924221821117,
          -2.289948912450747,
          -2.397736672250482,
          -2.499356564980556,
          -2.5899008827531285,
          -2.669267673896533,
          -2.738850729866976,
          -2.7951505785145234,
          -2.8377208418394777,
          -2.8663366494140776,
          -2.8794436653839237,
          -2.8776957629360793,
          -2.8595911987638174,
          -2.824526413361812,
          -2.7709179574840324,
          -2.696244378742531,
          -2.601035143764783,
          -2.485421930246041,
          -2.3457330933755687,
          -2.1773171084694902,
          -1.9903669536036461,
          -1.7854975400534367,
          -1.5570653153689051,
          -1.3173961752674428,
          -1.0613700065472569,
          -0.7895680456187398,
          -0.511874985937101,
          -0.21563107184882196,
          0.08619616904984623,
          0.3861972580418534,
          0.6989633706869209,
          1.0207778708357498,
          1.3340136554300601,
          1.647363864596315,
          1.9636364324608744,
          2.2709774468720036,
          2.5761679738693184,
          2.8833864721198497,
          3.183990907197781,
          3.4818681885855867,
          3.778698258048975,
          4.06841110373894,
          4.355047830106308,
          4.6371999480398,
          4.916395758076938,
          5.193492379308082,
          5.465895497959123,
          5.7385962611517,
          6.015746147238133,
          6.290191929925999,
          6.562553096291006,
          6.838310051198807,
          7.116597158078895,
          7.394019270287811,
          7.672057141573245,
          7.958146147804446,
          8.244931821960849,
          8.534882842226468,
          8.83530631478094,
          9.136302496739152,
          9.44406113805684,
          9.754740063000591,
          10.068058177803316,
          10.39105223878012,
          10.718506105259266,
          11.044796019125517,
          11.385180477162388,
          11.722801891058703,
          12.05320039379507,
          12.38368058333018,
          12.730029679732034,
          13.076882270802804,
          13.411874226214321,
          13.768707794190131,
          14.129101589668405,
          14.474625946615612,
          14.831333816580438,
          15.204381977351597,
          15.559623746703922,
          15.920784396862322,
          16.294087893959922,
          16.653143891585895,
          17.014040541042117,
          17.384905041853532,
          17.745210599431626,
          18.10701657019424,
          18.475855999380688,
          18.84630246801874,
          19.21472420232902,
          19.584540346121482,
          19.958100851664916,
          20.329597553521033,
          20.703147161033325,
          21.077787570745635,
          21.455960380519414,
          21.83415061963746,
          22.212369177737774,
          22.590516713945995,
          22.96436719868864,
          23.334278174377356,
          23.708226006935764,
          24.069648944614524,
          24.428433814823237,
          24.79761049909782,
          25.156074499134487,
          25.513139828635605,
          25.874825823022793,
          26.23221926054202,
          26.58051456533564,
          26.934570028422193,
          27.294888642306194,
          27.64325586475552,
          27.99604897895633,
          28.35418418730505,
          28.704773551893815,
          29.05658952341212,
          29.405256966231253,
          29.74381520410639,
          30.08952216504667,
          30.430189107576307,
          30.7686305982312,
          31.117670972715597,
          31.464284899047584,
          31.812090753528327,
          32.16944790293168,
          32.52699567878868,
          32.874598944993224,
          33.22732837432121,
          33.58027532993124,
          33.920839240893265,
          34.264828922228986,
          34.61128728634481,
          34.94589082877861,
          35.275329567294946,
          35.61041409457445,
          35.94043869854516,
          36.263390583040376,
          36.596066657461364,
          36.92665925182317,
          37.250184402734334,
          37.57994817482243,
          37.90020345663488,
          38.219552007931355,
          38.53980901236464,
          38.857577217796305,
          39.17250149844429,
          39.489643777499076,
          39.80358727079865,
          40.11781339224544,
          40.42924151967666,
          40.73622379955207,
          41.04445989472741,
          41.35088874478574,
          41.65497520405229,
          41.9614265250755,
          42.271072168318476,
          42.58123792493518,
          42.88786571829572,
          43.19305142909594,
          43.50057737772373,
          43.806329961741476,
          44.10132497765635,
          44.40195420490786,
          44.70752236099932,
          45.00281189532224,
          45.29845662417915,
          45.601799273884694,
          45.90751130700917,
          46.22640173857268,
          46.55017347414858,
          46.87469062819132,
          47.1914469307637,
          47.509470256328534,
          47.829164737400525,
          48.14280668634397,
          48.45386128703238,
          48.76420039518074,
          49.06519472456141,
          49.35004865653113,
          49.63000821728161,
          49.90821819677075,
          50.18827143675649,
          50.459815092181316,
          50.72820355268208,
          50.999958718424246,
          51.26788606915844,
          51.529091092358115,
          51.788276407407864,
          52.03588759590051,
          52.28029948126108,
          52.52381975742576,
          52.76955019493967,
          53.00974585183275,
          53.24282837028358,
          53.46962553471766,
          53.693679547011214,
          53.93955750395511,
          54.146748278555286,
          54.358127773173806,
          54.56898477118201,
          54.76912973935323,
          54.96387077493352,
          55.15659915367171,
          55.34248867620885,
          55.52535343603381,
          55.69920598625639,
          55.86621491056163,
          56.03220550731532,
          56.191473521787486,
          56.36291856370291,
          56.50561650020915,
          56.64437977042498,
          56.79340185676669,
          56.91837500975861,
          57.03138426467584,
          57.13356465682801,
          57.22602088932318,
          57.306044779724736,
          57.373374627639585,
          57.43217605875413,
          57.47720983081423,
          57.50457653292974,
          57.518346584204416,
          57.517745136272,
          57.500487446771686,
          57.47007387378284,
          57.43002968444119,
          57.377647365975996,
          57.31172282407779,
          57.23228604653392,
          57.134661511158505,
          57.02283434346222,
          56.902839022987706,
          56.76898220682917,
          56.61913788109337,
          56.45991171551233,
          56.287242736497,
          56.09977345872899,
          55.90374298983799,
          55.694997872309806,
          55.48467590340144,
          55.26874395373312,
          55.04751029904672,
          54.82045999010986,
          54.5954923019847,
          54.37309560019452,
          54.14158247539891,
          53.912583983921216,
          53.68682979856381,
          53.454702245081336,
          53.22027405095019,
          52.987656573905795,
          52.75257882631101,
          52.51185481929927,
          52.27302426442743,
          52.03078080113344,
          51.7850461427806,
          51.535293447741935,
          51.284703451296494,
          51.02929721836514,
          50.77101184539267,
          50.514173365922076,
          50.25228348169515,
          49.99072382687665,
          49.73213031797938,
          49.47005648043545,
          49.20333961606832,
          48.93857753061649,
          48.667908248004714,
          48.391078766366796,
          48.1154159957497,
          47.838437967857956,
          47.559067587884954,
          47.281372268163594,
          47.00132095405864,
          46.71760973445366,
          46.43593591471696,
          46.148292753451024,
          45.85632035163507,
          45.56862844645088,
          45.282904155000296,
          44.989302572254914,
          44.704910769193255,
          44.42901498775145,
          44.13873673718737,
          43.858723890277005,
          43.58039164446446,
          43.28891447462725,
          43.00576875020978,
          42.72864412225899,
          42.44265494073887,
          42.15898871057275,
          41.88689907876974,
          41.61368484837829,
          41.327364085667234,
          41.046209576389124,
          40.76926760918821,
          40.48166119739983,
          40.194410107886064,
          39.91605647677451,
          39.62920357923275,
          39.33792984507867,
          39.05339181290073,
          38.76237088309712,
          38.4649716455232,
          38.178118865473664,
          37.89437612941539,
          37.61095868416416,
          37.336097056222286,
          37.059832140687206,
          36.792794415777585,
          36.521075602631896,
          36.24654837775251,
          35.97019030513656,
          35.686331141051305,
          35.40642427889326,
          35.122147083347684,
          34.828857187409064,
          34.531376365016975,
          34.23472377670125,
          33.93274465898551,
          33.62964009170522,
          33.331536649326054,
          33.03132993227059,
          32.74293205246278,
          32.458982818919466,
          32.14237998376419,
          31.84724423609909,
          31.564821111582603,
          31.28608185163985,
          30.99343429225877,
          30.70429426182989,
          30.41737243083531,
          30.133758209340453,
          29.8382305747696,
          29.54635221663946,
          29.262143347438062,
          28.98076134509705,
          28.68571467674391,
          28.391921053556594,
          28.11188659467534,
          27.818004255932617,
          27.507904324632964,
          27.206354039645042,
          26.911777427116274,
          26.606186530568813,
          26.295056480866123,
          26.001851147523087,
          25.71810823123377,
          25.414931948480888,
          25.109368387626994,
          24.812703481004373,
          24.500925429686777,
          24.17977716141395,
          23.863600441803996,
          23.535817489830475,
          23.206757416779915,
          22.87973901683669,
          22.545880706805285,
          22.20427044091888,
          21.87027721572043,
          21.53078791872301,
          21.186893632697284,
          20.860359773882664,
          20.523793427818788,
          20.176538424821942,
          19.842862198609936,
          19.515026461287324,
          19.18573807860114,
          18.862686199628882,
          18.55648016665923,
          18.254130940050203,
          17.959637128272686,
          17.693546357961637,
          17.43255899973859,
          17.169570683985533,
          16.93550594306842,
          16.706753175460392,
          16.47809497246344,
          16.268830451164877,
          16.06851982986017,
          15.86680107248597,
          15.675349135262836,
          15.496831360608812,
          15.323160165364191,
          15.154540067823977,
          14.994344490690464,
          14.841959243213388,
          14.699499778565324,
          14.562038114444736,
          14.429925052762783,
          14.309649224771386,
          14.19974837828178,
          14.09281525672261,
          13.993474326854908,
          13.899836614039902,
          13.807523505040926,
          13.720160367754033,
          13.6394658713343,
          13.561564199439234,
          13.486552628367923,
          13.419424742245496,
          13.357006884840908,
          13.29439758194053,
          13.237246403268642,
          13.185012380973864,
          13.13124646089739,
          13.078802037518454,
          13.029589159916524,
          12.981466238682376,
          12.934984205905668,
          12.889845745152797,
          12.84617754646977,
          12.802311799011676,
          12.760668913530496,
          12.71760184302839,
          12.67377151391265,
          12.629442438187981,
          12.585999024896909,
          12.541943734308978,
          12.49921556714577,
          12.457245846960795,
          12.41509718658898,
          12.375730652571994,
          12.338253608650444,
          12.30393641953865,
          12.268642748119944,
          12.233768028973527,
          12.199364296666758,
          12.16415614209694,
          12.130178938237007,
          12.097122292398462,
          12.065817800076445,
          12.035992452837231,
          12.006532963544583,
          11.978500825586012,
          11.953501872204232,
          11.932815965296683,
          11.91329320756139,
          11.896007849020101,
          11.88341876043335,
          11.87442466711471,
          11.867866548338968,
          11.864990772143154,
          11.867153803251925,
          11.874609506538231,
          11.884294961902922,
          11.898923454501027,
          11.914961715370145,
          11.930796634704771,
          11.947213581796671,
          11.963619880648508,
          11.982247804514596,
          12.005729692428412,
          12.030458410889816,
          12.055371413336282,
          12.082351238999578,
          12.108712329648034,
          12.133241154011937,
          12.160475194187498,
          12.190017801922899,
          12.219956348312024,
          12.247621640343734,
          12.274406341192748,
          12.301076438098079,
          12.328609375867408,
          12.356533492138102,
          12.384076943385171,
          12.412500567823237,
          12.440592031673063,
          12.46926969789536,
          12.498346279275344,
          12.528319221798814,
          12.559454978675912,
          12.591555833550991,
          12.62432600353895,
          12.65542895869155,
          12.684652641170796,
          12.711778591617128,
          12.737357850368166,
          12.759273938751397,
          12.778740743505077,
          12.794658543587905,
          12.80794660003961,
          12.818119636231492,
          12.822140132166782,
          12.820026059043235,
          12.813528730161853,
          12.800612387586742,
          12.781655138724323,
          12.757536204330618,
          12.72991474814405,
          12.698511711481249,
          12.661985663036733,
          12.62089824419992,
          12.576494600555773,
          12.52967153342739,
          12.474534690002027,
          12.413906582724858,
          12.349826979581051,
          12.280737716352515,
          12.211218291269581,
          12.139716963289713,
          12.061824432406015,
          11.986364997791302,
          11.910639904622586,
          11.824844548804544,
          11.743863769929234,
          11.665871110660671,
          11.577252055411606,
          11.485051602653554,
          11.393171123223864,
          11.296277000318709,
          11.195578308255824,
          11.09789480115782,
          11.000593540045958,
          10.89974334016699,
          10.79478199233719,
          10.688647086583925,
          10.579899533922429,
          10.46876836558437,
          10.35834152951342,
          10.24604010401854,
          10.135789428545994,
          10.024426354590814,
          9.915408777931122,
          9.809892677074464,
          9.690502556628143,
          9.568845010186527,
          9.44948845425078,
          9.329345825764314,
          9.210788423624953,
          9.094740096593306,
          8.981250760713174,
          8.869008724662915,
          8.759087914090877,
          8.654570927896945,
          8.558440799660923,
          8.466489237235667,
          8.37694196219669,
          8.288965865742293,
          8.199190543994659,
          8.109330310369584,
          8.022090972547874,
          7.934504286438223,
          7.846448633167835,
          7.760029696434877,
          7.6723880755626,
          7.584815270506617,
          7.496686799929899,
          7.407182621643937,
          7.317985356212052,
          7.2353434867070066,
          7.152570059125531,
          7.0710588167918935,
          6.99677753000603,
          6.923162654023745,
          6.854308092054447,
          6.790927212107014,
          6.730942123001968,
          6.6746098504638915,
          6.624191221291647,
          6.578235463220679,
          6.53568360116851,
          6.499806109005132,
          6.469925867811654,
          6.444626735024947,
          6.425174858766019,
          6.41130754770066,
          6.404394650407598,
          6.404731373174716,
          6.411926150723632,
          6.426463929379376,
          6.449763435402024,
          6.481803466196001,
          6.5234848931937,
          6.57586273086052,
          6.639274138436655,
          6.714297420238251,
          6.8009625620786265,
          6.90357961841715,
          7.020815263863826,
          7.149711280344686,
          7.296393538330737,
          7.462987255751147,
          7.641623185464991,
          7.8287948857142124,
          8.044999776456184,
          8.28775859286178,
          8.535562218000656,
          8.792808696598971,
          9.06682767516232,
          9.339638558131611,
          9.619226296623978,
          9.90699890156163,
          10.193880604205342,
          10.485797678629408,
          10.796644596607308,
          11.070419359678132,
          11.350216718684798,
          11.629109942162875,
          11.901352374105752,
          12.169770891789925,
          12.430130313416093,
          12.682173623610057,
          12.928658888705487,
          13.167277353948695,
          13.401859977525756,
          13.627224026174238,
          13.84808027205692,
          14.062692975073334,
          14.268134588907262,
          14.471169548669833,
          14.669167292320772,
          14.8608675302553,
          15.051004870162453,
          15.235143071635735,
          15.415890054492111,
          15.598363106013123,
          15.778062308897118,
          15.956238195706161,
          16.137684244592446,
          16.31997576246259,
          16.503687983755558,
          16.69005559798489,
          16.87882971366824,
          17.07319447522499,
          17.270317689560514,
          17.468839201329406,
          17.671602490253267,
          17.87897598609055,
          18.090712455672396,
          18.30765249090772,
          18.528780803642082,
          18.756977050385643,
          18.994609254251344,
          19.232421288610336,
          19.477242452508207,
          19.733908815230023,
          19.989288532694463,
          20.249931476722182,
          20.51197771340003,
          20.78705618039728,
          21.061403124296426,
          21.33083236390065,
          21.61857787570625,
          21.906607252471186,
          22.185178090997447,
          22.473137670441695,
          22.774031558632206,
          23.067130972314928,
          23.361836180778283,
          23.66836859448006,
          23.971027775377983,
          24.269749084419086,
          24.578033814122037,
          24.8858323012305,
          25.188334065545572,
          25.498649613846748,
          25.80548880478919,
          26.118879041891603,
          26.433331971708736,
          26.743520835196794,
          27.056669054485372,
          27.372039579355043,
          27.687009174724732,
          28.000868542639235,
          28.32254383953865,
          28.64040950241382,
          28.957066871469387,
          29.277448768422754,
          29.59241592452326,
          29.902026466826495,
          30.21071923414979,
          30.51748793933198,
          30.81424518134586,
          31.115312893397437,
          31.41691701548777,
          31.70935462994214,
          32.01002736632239,
          32.305487686362774,
          32.59175093012523,
          32.88108925124949,
          33.17164525781489,
          33.46162107819969,
          33.74158875561453,
          34.02100002905836,
          34.305183666129366,
          34.5799553017979,
          34.850607264477475,
          35.112672686025306,
          35.361655041668115,
          35.61005739853109,
          35.84955917601088,
          36.08065467694008,
          36.30674445473008,
          36.52828429164542,
          36.740786993766555,
          36.950978128104765,
          37.1515263566296,
          37.3379031196239,
          37.51386446547182,
          37.677077230058806,
          37.82778807464054,
          37.966008424912935,
          38.11130017116466,
          38.23093466869777,
          38.33561346131356,
          38.43143108582396,
          38.519650293463094,
          38.59730815158196,
          38.667173203124555,
          38.72823633779689,
          38.780231826800176,
          38.82131391856022,
          38.8537240151622,
          38.877803819647404,
          38.894234864962385,
          38.90159752065538,
          38.89953729044153,
          38.890052082037606,
          38.87367813816234,
          38.84854955248623,
          38.81797434746558,
          38.779441676028604,
          38.73501562451974,
          38.6864053617166,
          38.6335014144021,
          38.57785177822729,
          38.517439602618225,
          38.45287013695489,
          38.38402128169546,
          38.30882886427461,
          38.230177988295075,
          38.15059225832807,
          38.065486871257875,
          37.976527684340674,
          37.884758965332885,
          37.7878007505029,
          37.685561069492735,
          37.5804973011744,
          37.477257537827064,
          37.3713607379538,
          37.26225480359238,
          37.155321347240104,
          37.04618385764532,
          36.93476024600219,
          36.82306572527969,
          36.71047495261248,
          36.60347725647842,
          36.493653492177515,
          36.38721544580902,
          36.28899847501084,
          36.187005267077254,
          36.09139940740021,
          35.99904055330144,
          35.90677109545825,
          35.82346517571844,
          35.749401535921855,
          35.672391822966624,
          35.60268346879452,
          35.541761543344734,
          35.48030599214533,
          35.42566726058668,
          35.37888302380268,
          35.333398957189836,
          35.2946347743286,
          35.26039733908834,
          35.23183590435802,
          35.20940945821903,
          35.18965660954598,
          35.17240261894478,
          35.15775757130984,
          35.14392850831232,
          35.13013122461834,
          35.11606018872258,
          35.102360036807724,
          35.098107667433965,
          35.09449582923006,
          35.09129154278542,
          35.088055727967266,
          35.08522575229344,
          35.082758732141116,
          35.08035372730898,
          35.07813168641757,
          35.07620098611242,
          35.07460852969232,
          35.05984971422305,
          35.04339496355989,
          35.02667244107595,
          35.00962336343616,
          34.99226311457334,
          34.974576565465476,
          34.95656525119766,
          34.93827142952938,
          34.91943288048625,
          34.90014012752183,
          34.895416468441276,
          34.89234186534965,
          34.88915666286287,
          34.88598630017445,
          34.88281658910924,
          34.87956137744027,
          34.87633219304776,
          34.87307011284546,
          34.86976703210665,
          34.86644475581382,
          34.8551747366878,
          34.8429768893144,
          34.83070422844722,
          34.818430484206424,
          34.806125256584295,
          34.79378574988798,
          34.781432463025915,
          34.76903933762169,
          34.75661634860349,
          34.74412907053127,
          34.7397093680804,
          34.73609114357576,
          34.732428863718184,
          34.72880953363549,
          34.72522656296134,
          34.72155208566735,
          34.71785899180338,
          34.71419676103996,
          34.71044181848479,
          34.706710040852414,
          34.68587287380501,
          34.66277496472863,
          34.63964893091603,
          34.61657909776959,
          34.59361775950861,
          34.57065433245965,
          34.54759662177167,
          34.52461395494192,
          34.50171177409114,
          34.47853041139153,
          34.47362277545028,
          34.47080664475168,
          34.46805739335795,
          34.46543050703443,
          34.462802817358906,
          34.46018330417802,
          34.45752989679673,
          34.45458549870025,
          34.451876702902915,
          34.44921957873822,
          34.4485014385168,
          34.44782136311084,
          34.447247605163966,
          34.446667736507294,
          34.445973827983906,
          34.44530600473072,
          34.44469594169167,
          34.444056801391554,
          34.443373638260226
         ],
         "yaxis": "y"
        },
        {
         "line": {
          "color": "black"
         },
         "mode": "lines",
         "name": "Optimized Path",
         "type": "scatter",
         "x": [
          -34.20561757044228,
          -34.20512760429347,
          -34.20454790552907,
          -34.2039475820338,
          -34.203528029543456,
          -34.20318769697766,
          -34.20250008828952,
          -34.201887393251134,
          -34.20110695414667,
          -34.20043328331251,
          -34.199797365257,
          -34.19902567216335,
          -34.19822373944125,
          -34.19756620269559,
          -34.19691395620989,
          -34.19612628784581,
          -34.19539587647322,
          -34.19464752519713,
          -34.19413826717369,
          -34.19362218978343,
          -34.19308286816422,
          -34.19247713345691,
          -34.1919654756452,
          -34.19138345574506,
          -34.190871769903445,
          -34.19032247122443,
          -34.18980320715251,
          -34.18935691811098,
          -34.18894357394385,
          -34.188490371118526,
          -34.188142308575856,
          -34.18779060926308,
          -34.187408824528056,
          -34.18704889979322,
          -34.18660587485973,
          -34.186197158312446,
          -34.185842641909616,
          -34.18554050023449,
          -34.185178222994665,
          -34.18478562614525,
          -34.1845163518966,
          -34.184152676221,
          -34.183672892900894,
          -34.18341526313705,
          -34.18317743785774,
          -34.182904178641174,
          -34.18255394965871,
          -34.18229836253587,
          -34.18202343423894,
          -34.18168564101408,
          -34.18137437935082,
          -34.180999760656505,
          -34.18063044088135,
          -34.1803417108544,
          -34.18004184497972,
          -34.17974380811583,
          -34.17939100594898,
          -34.179096825713465,
          -34.17889403629774,
          -34.17857668929551,
          -34.17836158297033,
          -34.178069181253385,
          -34.17775251387628,
          -34.17751570665378,
          -34.17725998686529,
          -34.176965245194936,
          -34.17669134606577,
          -34.17606814416233,
          -34.17522295581092,
          -34.174452355660485,
          -34.17371311972212,
          -34.17281768998747,
          -34.171850618743974,
          -34.17098917190925,
          -34.170173012591064,
          -34.169262807754016,
          -34.168241223649744,
          -34.16753996547593,
          -34.166801221654865,
          -34.165990313703595,
          -34.165372902431336,
          -34.16463275076087,
          -34.16372519837798,
          -34.163001524746676,
          -34.16231107211428,
          -34.16138802048847,
          -34.16053081643791,
          -34.15958643540004,
          -34.15848955858913,
          -34.157424462718645,
          -34.1563743189374,
          -34.1553950611015,
          -34.15438764173777,
          -34.15330519898663,
          -34.15229595639603,
          -34.15128403563302,
          -34.15032583585512,
          -34.14940720504957,
          -34.148747773708,
          -34.148157429515166,
          -34.14737296142082,
          -34.146622897467466,
          -34.14609913542775,
          -34.145519128021874,
          -34.14502975057139,
          -34.144284896489644,
          -34.143434800923956,
          -34.14280878290143,
          -34.142058943459496,
          -34.14131342461109,
          -34.140581272596584,
          -34.139696783478215,
          -34.138875008191974,
          -34.13819982788251,
          -34.13745784699546,
          -34.13665333234713,
          -34.135783958014784,
          -34.1349121329733,
          -34.13429143553747,
          -34.13368132261655,
          -34.132894153643726,
          -34.13206479282877,
          -34.131356852160444,
          -34.13073211020393,
          -34.129958414662426,
          -34.12910768001923,
          -34.12829256670085,
          -34.12767517785592,
          -34.12722646375426,
          -34.12646961049529,
          -34.125659878715005,
          -34.125128620572006,
          -34.12447133849393,
          -34.12358465970485,
          -34.123023731530715,
          -34.12210246976016,
          -34.12151730651414,
          -34.12098252068224,
          -34.12066488981601,
          -34.11994193737324,
          -34.119172869338506,
          -34.11881621364209,
          -34.1182378633531,
          -34.11754844375961,
          -34.11683706421001,
          -34.11598998946467,
          -34.11525392540833,
          -34.11469304205291,
          -34.11388298715692,
          -34.11270671221946,
          -34.112151292684246,
          -34.111601557295415,
          -34.11083929244948,
          -34.11001892168905,
          -34.109320386475915,
          -34.10880792155222,
          -34.10840442199014,
          -34.10808228712271,
          -34.10735719121386,
          -34.10673042576127,
          -34.106331790496746,
          -34.10589372950673,
          -34.105172678418185,
          -34.10426190981686,
          -34.103003041120786,
          -34.10241863646337,
          -34.10185535156437,
          -34.100838685205716,
          -34.09928819133874,
          -34.09708354240105,
          -34.09556069941669,
          -34.09431089634316,
          -34.09250476578938,
          -34.09060968110186,
          -34.08888225864368,
          -34.08717589837203,
          -34.085444038845665,
          -34.083816814136235,
          -34.08219763196009,
          -34.08048540458973,
          -34.07889818574541,
          -34.07733461922295,
          -34.07566360130542,
          -34.073918629785176,
          -34.07229456398648,
          -34.07055171459505,
          -34.06880304173993,
          -34.06740468816458,
          -34.06625705097835,
          -34.06494957727392,
          -34.06342972415235,
          -34.06188819030862,
          -34.06043797807096,
          -34.059363132909475,
          -34.058109234914646,
          -34.05662927587014,
          -34.055258540792856,
          -34.054034104321765,
          -34.05312530342876,
          -34.05198121342687,
          -34.0504555867898,
          -34.04948585276847,
          -34.048398485563695,
          -34.04709464880089,
          -34.0454102457629,
          -34.04266646319351,
          -34.0409465339217,
          -34.03835988273773,
          -34.03597418314847,
          -34.0336651065715,
          -34.026657465890594,
          -34.0128748956983,
          -33.98879699105395,
          -33.95120492104014,
          -33.89847043071538,
          -33.83217480926878,
          -33.759082516147195,
          -33.688152090901596,
          -33.62902239804277,
          -33.581904201912735,
          -33.54761355832541,
          -33.521976425812205,
          -33.503625704206605,
          -33.49091867870461,
          -33.479746893959316,
          -33.46613840600857,
          -33.44623741792179,
          -33.41348354991016,
          -33.366492860284716,
          -33.304430002101135,
          -33.2265010859668,
          -33.13328627029537,
          -33.026047374446584,
          -32.904400659034586,
          -32.76791621366324,
          -32.61504638432957,
          -32.444588303201385,
          -32.257641503338114,
          -32.057264055099246,
          -31.845896423892555,
          -31.62169938902757,
          -31.382115349269377,
          -31.134352270515613,
          -30.880264731544443,
          -30.621592093416492,
          -30.35452716825152,
          -30.084251738630325,
          -29.814435917332784,
          -29.535859682475248,
          -29.26008893727225,
          -28.98908448934071,
          -28.711604365075154,
          -28.437710308015056,
          -28.167123579287267,
          -27.903511142314834,
          -27.640916520907638,
          -27.384319979531227,
          -27.14404416686677,
          -26.909325595507926,
          -26.681111574104893,
          -26.465553354460898,
          -26.262944822222714,
          -26.071024748783216,
          -25.896680086140506,
          -25.739502325773667,
          -25.597339361397758,
          -25.469877735215118,
          -25.359166951779105,
          -25.269094561371322,
          -25.19209099554038,
          -25.13037068292393,
          -25.09191261411201,
          -25.069700809315894,
          -25.06395870061066,
          -25.074761203703314,
          -25.100204339113603,
          -25.137218874930355,
          -25.18718783476567,
          -25.24978584704496,
          -25.317153382883465,
          -25.39510282737947,
          -25.484067165473096,
          -25.57582872449151,
          -25.675141800072094,
          -25.785155098916132,
          -25.899992780062643,
          -26.02146982739026,
          -26.151192080146767,
          -26.287612712018074,
          -26.42813875081477,
          -26.57531957852832,
          -26.73030498687557,
          -26.886367542777563,
          -27.046764994992802,
          -27.21833001407868,
          -27.392179771408387,
          -27.570118001596843,
          -27.754507213233985,
          -27.950860643741503,
          -28.13744686676629,
          -28.32731941259005,
          -28.525896778413372,
          -28.71960461455676,
          -28.91003404390529,
          -29.10566392179609,
          -29.30564275628184,
          -29.495330460098923,
          -29.68888344896392,
          -29.887600083069856,
          -30.079538241210784,
          -30.26661584695017,
          -30.45954199955235,
          -30.648351976094574,
          -30.830012935363236,
          -31.017014787628053,
          -31.201843391943203,
          -31.38726115318541,
          -31.569889064281064,
          -31.75503809481409,
          -31.941639224946446,
          -32.12293501781387,
          -32.30373019515281,
          -32.479155690728824,
          -32.66034617134181,
          -32.82886258580736,
          -32.99644742433231,
          -33.170881164548135,
          -33.337583190309445,
          -33.499261533426264,
          -33.66113989274895,
          -33.8264744454099,
          -33.98787157382627,
          -34.14278176975569,
          -34.29897856697425,
          -34.453265970126935,
          -34.605058507221436,
          -34.75402248432084,
          -34.90301103772693,
          -35.04775593067414,
          -35.18872387727439,
          -35.33140545605798,
          -35.463404703490355,
          -35.59117549177854,
          -35.720451508688384,
          -35.8435311671989,
          -35.95921239213348,
          -36.07599763476948,
          -36.186211537122986,
          -36.28911837561348,
          -36.38976082163263,
          -36.48056851922742,
          -36.565927578444594,
          -36.64488302557363,
          -36.71523314991207,
          -36.78012984628027,
          -36.841769117004866,
          -36.89603652639348,
          -36.946037299585576,
          -36.99486233621137,
          -37.03741023356843,
          -37.07801470893926,
          -37.11690550027645,
          -37.15317238300912,
          -37.188491887268846,
          -37.22497997271774,
          -37.26155949805779,
          -37.298584975356945,
          -37.33759753421884,
          -37.376077634267816,
          -37.41258936031957,
          -37.44838660622586,
          -37.48300805057889,
          -37.51739476319382,
          -37.55267565865365,
          -37.58875856088244,
          -37.62609696041984,
          -37.665195715488586,
          -37.70594469185669,
          -37.74892679149871,
          -37.79219388880461,
          -37.8378527933611,
          -37.884237089227575,
          -37.93068842754541,
          -37.978499241950765,
          -38.030999184382026,
          -38.086470630036565,
          -38.14112251571634,
          -38.20331311821484,
          -38.26065790686239,
          -38.31602276906785,
          -38.37248345049218,
          -38.430691674291126,
          -38.48720945720995,
          -38.544139784274144,
          -38.60167691584601,
          -38.66074969657934,
          -38.72056922037399,
          -38.782622426839275,
          -38.84408807873072,
          -38.907387780298954,
          -38.9740301194087,
          -39.03879585844459,
          -39.10734523055302,
          -39.1828198754861,
          -39.26188093301199,
          -39.34274627729819,
          -39.432958033968546,
          -39.525947432600134,
          -39.6212713935699,
          -39.73086413311233,
          -39.84499137207389,
          -39.962527898239294,
          -40.09329713891962,
          -40.230802602702255,
          -40.372889353100234,
          -40.527385513557775,
          -40.68354228401489,
          -40.84828850045461,
          -41.0254641616563,
          -41.20078019583397,
          -41.387720825838066,
          -41.59004337321235,
          -41.79219816931896,
          -42.00869827938041,
          -42.24539198990937,
          -42.484668380759224,
          -42.73662447826301,
          -43.00114416394548,
          -43.27609452432519,
          -43.56481912633542,
          -43.872609957200716,
          -44.1693705404054,
          -44.46503290335496,
          -44.78204638662235,
          -45.0903708313035,
          -45.389688917183896,
          -45.70721401650844,
          -46.01449876014241,
          -46.301933990162915,
          -46.5928799282053,
          -46.878278503481994,
          -47.15099380296704,
          -47.415478539240446,
          -47.6679250249944,
          -47.90793035440927,
          -48.141185365189216,
          -48.36129979155681,
          -48.56970213554213,
          -48.76957357090377,
          -48.95917637108032,
          -49.138204288159045,
          -49.31027172223736,
          -49.47066745504553,
          -49.622680692705416,
          -49.767410520606916,
          -49.90190489333228,
          -50.02881817334456,
          -50.1506213795373,
          -50.267191345817075,
          -50.38086896087241,
          -50.49376203664987,
          -50.608163853918185,
          -50.72401842175004,
          -50.84244240574792,
          -50.963751019578346,
          -51.08983043878479,
          -51.22075674893193,
          -51.35900562531298,
          -51.50906280459484,
          -51.66635719129263,
          -51.83105697024285,
          -52.00717503961635,
          -52.188688529726036,
          -52.37242421765366,
          -52.56709421064206,
          -52.773474958964805,
          -52.97892257285614,
          -53.195123381676176,
          -53.42681577712202,
          -53.649910780207875,
          -53.88451912230249,
          -54.13223293236011,
          -54.37460480163445,
          -54.629416172263774,
          -54.894364243322975,
          -55.14641611317685,
          -55.40506948288841,
          -55.6716570181352,
          -55.922705028940356,
          -56.17810759978741,
          -56.45321031865366,
          -56.7201638563687,
          -56.97808654414694,
          -57.25424099397908,
          -57.530213492589006,
          -57.79258684599805,
          -58.06926282313392,
          -58.349819335344705,
          -58.616750299832695,
          -58.88732139066519,
          -59.159086273397115,
          -59.41794493152703,
          -59.67696311829514,
          -59.93524212644045,
          -60.18963265574833,
          -60.445610170856284,
          -60.701419088223226,
          -60.95504493480911,
          -61.21153464433444,
          -61.465873569219475,
          -61.72036104617876,
          -61.972811903378805,
          -62.225017583114415,
          -62.47134097875486,
          -62.71335073223099,
          -62.95098370756537,
          -63.180162311978606,
          -63.40013121217142,
          -63.614687223332176,
          -63.82479531230667,
          -64.03329465455552,
          -64.24406272880509,
          -64.45625782342314,
          -64.66556219238166,
          -64.87026423892154,
          -65.06956097464109,
          -65.26413631925908,
          -65.46059588017901,
          -65.65490575539503,
          -65.84367197770793,
          -66.02220358487762,
          -66.19413132258474,
          -66.36399270954566,
          -66.53266854105782,
          -66.70051426694702,
          -66.86400963304442,
          -67.0258983849939,
          -67.18579003191651,
          -67.33930976604466,
          -67.49264233865657,
          -67.6493452168336,
          -67.80094813227709,
          -67.94931241038378,
          -68.09844525743789,
          -68.2487474904265,
          -68.39589637121036,
          -68.54040290713341,
          -68.6826353460433,
          -68.8183367994397,
          -68.9489152643788,
          -69.08132083452956,
          -69.21092947082028,
          -69.33548314964287,
          -69.46049604747336,
          -69.58185184846917,
          -69.69362773715109,
          -69.8067214135986,
          -69.91712302018885,
          -70.02196333199016,
          -70.1288564870053,
          -70.23515589674767,
          -70.33463397310949,
          -70.43577245998249,
          -70.53622732540317,
          -70.63223798341733,
          -70.73156769828218,
          -70.82895939543982,
          -70.92245067205916,
          -71.01812746600336,
          -71.11129764816239,
          -71.20210707045638,
          -71.29436376759374,
          -71.38657745020753,
          -71.48054413206515,
          -71.57735010220847,
          -71.67422081859812,
          -71.76958137297436,
          -71.86815681626645,
          -71.96324078243423,
          -72.05808794141366,
          -72.15075367355747,
          -72.23538300654613,
          -72.3172211523773,
          -72.39269759781176,
          -72.4555167203586,
          -72.5104650780865,
          -72.55810370146347,
          -72.59489616614175,
          -72.62159065848107,
          -72.63975840705338,
          -72.6497529077105,
          -72.65224454910688,
          -72.64372445092144,
          -72.62802140267841,
          -72.60428635492597,
          -72.57200414560242,
          -72.53598392872436,
          -72.49531034686584,
          -72.4486386120134,
          -72.39588093509896,
          -72.33560353735982,
          -72.27111568484752,
          -72.20093793747819,
          -72.12291088238662,
          -72.03903957638944,
          -71.94796436942242,
          -71.84852238273824,
          -71.74858084124595,
          -71.6332122852996,
          -71.50002467744615,
          -71.3639000574612,
          -71.21504056848309,
          -71.04432374782473,
          -70.87186353529634,
          -70.70006983579766,
          -70.50740459203469,
          -70.30066096169622,
          -70.08982898006605,
          -69.85721683152681,
          -69.60581928650862,
          -69.35221098806976,
          -69.0872216975325,
          -68.80662929845899,
          -68.51546197996846,
          -68.21009619484687,
          -67.89401674493533,
          -67.56731518926061,
          -67.2252024176128,
          -66.87492859708027,
          -66.52184388554022,
          -66.15251578092575,
          -65.76952733798213,
          -65.38416451188696,
          -64.99594837258051,
          -64.59321183200468,
          -64.18884442630625,
          -63.811600619865764,
          -63.42288931395214,
          -63.01624508767463,
          -62.64152953678123,
          -62.2640666791697,
          -61.853317592866794,
          -61.46500081063432,
          -61.08532152543534,
          -60.67614560631991,
          -60.278129799393,
          -59.884513000214504,
          -59.47114448678991,
          -59.06483706492197,
          -58.666134233806375,
          -58.260466515774944,
          -57.85924175400575,
          -57.460730879351644,
          -57.05784778303783,
          -56.65216634152449,
          -56.24967960194449,
          -55.84581873091747,
          -55.44815547419902,
          -55.052092128106615,
          -54.66085908411506,
          -54.26291846472017,
          -53.871946508503974,
          -53.47772906935791,
          -53.08057496209116,
          -52.69119362573196,
          -52.31307326450289,
          -51.923414829847125,
          -51.55950949536136,
          -51.207830192801644,
          -50.84093883846838,
          -50.49204521980163,
          -50.14344131050435,
          -49.77948774904636,
          -49.43017201488649,
          -49.08340048155227,
          -48.69173333570923,
          -48.34133732481832,
          -47.995854895310224,
          -47.63904047154031,
          -47.2728492181963,
          -46.91690442804988,
          -46.56092988530211,
          -46.195362154793386,
          -45.83653714396913,
          -45.48547058399427,
          -45.124833690094285,
          -44.76351168082494,
          -44.41093447816134,
          -44.049341516020974,
          -43.68533322212456,
          -43.33408925432588,
          -42.98191301291801,
          -42.63227271458896,
          -42.297458368977836,
          -41.957143229546375,
          -41.62223188374709,
          -41.291430313327695,
          -40.954228962864995,
          -40.61244750504851,
          -40.26365841179854,
          -39.91746402724253,
          -39.565673344191794,
          -39.20039404198487,
          -38.82819536532496,
          -38.451998976616736,
          -38.073731729118414,
          -37.692383651950195,
          -37.30834384334934,
          -36.92657384677088,
          -36.55511111050676,
          -36.18682623258284,
          -35.81271986813442,
          -35.44236500443909,
          -35.07719525981692,
          -34.70534660570074,
          -34.329309988475934,
          -33.95439710123461,
          -33.57987473620433,
          -33.207241277978454,
          -32.81504103111591,
          -32.431353744027135,
          -32.059889510799664,
          -31.66570261798346,
          -31.271381983330798,
          -30.910961686079972,
          -30.527924061534268,
          -30.130132589322397,
          -29.76505216077786,
          -29.400547957043873,
          -29.016938705416603,
          -28.656525429300615,
          -28.329218485812287,
          -27.97424408178218,
          -27.616340026906627,
          -27.288527481947636,
          -26.94552486918197,
          -26.598130779161686,
          -26.271703671420283,
          -25.940302877460553,
          -25.61588364589193,
          -25.300940871294408,
          -24.989829850443677,
          -24.68433470046486,
          -24.395699014681064,
          -24.107083793074718,
          -23.831048492865037,
          -23.5716359513729,
          -23.302969298821715,
          -23.03913392308083,
          -22.794603442449816,
          -22.5552067675838,
          -22.320274036579058,
          -22.09706591076508,
          -21.889360945408974,
          -21.687582386626527,
          -21.503739452482794,
          -21.33699740777679,
          -21.17906702782219,
          -21.032342953580972,
          -20.904274164261622,
          -20.7852065655937,
          -20.675111681466376,
          -20.58038576204182,
          -20.494987813321163,
          -20.424543775185434,
          -20.369521301243612,
          -20.32778348630391,
          -20.301372124137583,
          -20.290567430834937,
          -20.29368962038936,
          -20.308198730708714,
          -20.33540061225545,
          -20.37386703665702,
          -20.421659905577652,
          -20.47593434402756,
          -20.53758723670193,
          -20.60642808792559,
          -20.680183954183804,
          -20.75776454402994,
          -20.83978984455303,
          -20.928601994800303,
          -21.024117224113652,
          -21.12296310318474,
          -21.220500724220777,
          -21.32168127111698,
          -21.42744980385682,
          -21.528942427912764,
          -21.634378590709453,
          -21.74217623346717,
          -21.850195175055266,
          -21.955570731659417,
          -22.06388804448218,
          -22.170560273902325,
          -22.27407383348731,
          -22.382967638474106,
          -22.4925149597515,
          -22.599065162893176,
          -22.708665111122727,
          -22.8205675553048,
          -22.931634332948207,
          -23.04140948060133,
          -23.154014483046176,
          -23.26637901700943,
          -23.376624767611364,
          -23.4902370038099,
          -23.603200317860484,
          -23.71334714780898,
          -23.82266886687317,
          -23.93029049379185,
          -24.038336944674572,
          -24.149188868153907,
          -24.256472663897387,
          -24.363898751880633,
          -24.474573907058865,
          -24.582892558222987,
          -24.690156388425507,
          -24.796890856674764,
          -24.90411437220659,
          -25.01201872208549,
          -25.122113714063985,
          -25.232789670764756,
          -25.34418579036815,
          -25.459784354752852,
          -25.57620761824168,
          -25.694946343991376,
          -25.817599642611988,
          -25.9413085051037,
          -26.066936002154012,
          -26.19706329518293,
          -26.32595914993584,
          -26.459489960937468,
          -26.601541244681247,
          -26.74275048851859,
          -26.888385569412215,
          -27.04218815800793,
          -27.202602317061192,
          -27.35577720375166,
          -27.516671766379552,
          -27.682944697420943,
          -27.845102592808274,
          -28.00796474243966,
          -28.17274308615302,
          -28.34023289729439,
          -28.500565227029785,
          -28.66232227715479,
          -28.82531492102295,
          -28.98318192323284,
          -29.143036716681856,
          -29.306655581984884,
          -29.4718442800354,
          -29.63385378808072,
          -29.79608649738163,
          -29.961653524281843,
          -30.126446349891978,
          -30.2957713753911,
          -30.46280090623393,
          -30.632082760341724,
          -30.803925200921448,
          -30.968043344124233,
          -31.13383621297871,
          -31.301162516675138,
          -31.468852141513388,
          -31.631743910557933,
          -31.796441075882125,
          -31.965584640409897,
          -32.14833293033363,
          -32.31169447231609,
          -32.478993527224304,
          -32.64902287211386,
          -32.815287145159246,
          -32.975320701313485,
          -33.13505501637585,
          -33.29120205433395,
          -33.441914696308004,
          -33.59105718495849,
          -33.735973601338095,
          -33.87465035676541,
          -34.00427994875884,
          -34.131091904112985,
          -34.252362061489286,
          -34.3630693642207,
          -34.47336982364717,
          -34.58286223788178,
          -34.685704274603715,
          -34.786078286924045,
          -34.88827383593227,
          -34.98373788858449,
          -35.07424027594026,
          -35.166704351451514,
          -35.25208013037038,
          -35.3308165106297,
          -35.4101595569824,
          -35.48416554115981,
          -35.55142340097925,
          -35.6202453861711,
          -35.68968285234464,
          -35.75289694299259,
          -35.824094886915425,
          -35.89136759882674,
          -35.94968688652356,
          -36.008249596315906,
          -36.065589915635414,
          -36.118317987507425,
          -36.16969494296698,
          -36.222088346329805,
          -36.273165347559356,
          -36.323530074248744,
          -36.374673453579675,
          -36.4236215397993,
          -36.470225773011755,
          -36.515395573226314,
          -36.5577760656214,
          -36.59852145020301,
          -36.63780472140653,
          -36.676010107139824,
          -36.714076889677585,
          -36.751293158262406,
          -36.788997442630574,
          -36.82675897923843,
          -36.866198737719344,
          -36.905451275148295,
          -36.94429329164378,
          -36.98460902868335,
          -37.025025379994595,
          -37.065409761868935,
          -37.10865523908023,
          -37.155461102019125,
          -37.20353647817547,
          -37.25157198262911,
          -37.30062393083243,
          -37.35073523680281,
          -37.40123512065318,
          -37.453051846566204,
          -37.50717640957091,
          -37.562629870881366,
          -37.61676335648442,
          -37.672537690070804,
          -37.72776860651589,
          -37.78408638175532,
          -37.84052927721857,
          -37.897093478155405,
          -37.95330166201434,
          -38.01125301151972,
          -38.071293117480295,
          -38.12995578170714,
          -38.1899408145891,
          -38.25028469790277,
          -38.31046471589048,
          -38.378134869548575,
          -38.440349644564876,
          -38.502398485575746,
          -38.568505903985056,
          -38.64070355117893,
          -38.718004924913664,
          -38.798034410615564,
          -38.886119712661454,
          -38.98175935053867,
          -39.0792656495281,
          -39.18640041717412,
          -39.302336197043665,
          -39.41611697571312,
          -39.53847524404857,
          -39.67173282772624,
          -39.80518618284488,
          -39.94576151338095,
          -40.09793918827699,
          -40.2534738635743,
          -40.41798295828943,
          -40.5925092383742,
          -40.7750465306845,
          -40.967669750246635,
          -41.174281781029805,
          -41.39035522092231,
          -41.622582145892046,
          -41.86528641863914,
          -42.11695153836835,
          -42.37669364414768,
          -42.64749591458337,
          -42.93708228422639,
          -43.22370060867796,
          -43.50647753263288,
          -43.81115578117619,
          -44.11800141268965,
          -44.41584984317279,
          -44.72360411818214,
          -45.03380834625305,
          -45.33381904642938,
          -45.63846832439477,
          -45.93757090775836,
          -46.22087270613417,
          -46.5035711566294,
          -46.77893332517433,
          -47.0343150457652,
          -47.27939174702824,
          -47.51675722133514,
          -47.734860012290014,
          -47.94634545524114,
          -48.150103336025424,
          -48.335769837534514,
          -48.51310542120231,
          -48.682150875261904,
          -48.83516736394039,
          -48.979383748674465,
          -49.11591484749563,
          -49.241701242482264,
          -49.35943228833208,
          -49.471916464854864,
          -49.579275885315106,
          -49.68140555403737,
          -49.78068342554034,
          -49.87876999000025,
          -49.97746400314953,
          -50.07987937357662,
          -50.18702396270841,
          -50.30061060505931,
          -50.4190670660807,
          -50.54167523643701,
          -50.668310228884216,
          -50.797953441456606,
          -50.93191387947032,
          -51.06994160759672,
          -51.21266111259615,
          -51.362440538875454,
          -51.51674988472523,
          -51.67432768509761,
          -51.84114265664589,
          -52.009844684999905,
          -52.18063095458253,
          -52.354294153950086,
          -52.537658325279395,
          -52.723674366177775,
          -52.90765586066133,
          -53.10627122377588,
          -53.30947140228061,
          -53.50495036559547,
          -53.70962865698191,
          -53.92714645252598,
          -54.13864078241311,
          -54.356556979290815,
          -54.58711562939852,
          -54.811027595367385,
          -55.0332942622891,
          -55.26607397218623,
          -55.499364896850125,
          -55.72975936842476,
          -55.9657624271867,
          -56.20831832678944,
          -56.45031950148498,
          -56.692888409526255,
          -56.93865140555208,
          -57.189295935363894,
          -57.43666875487494,
          -57.68549157026442,
          -57.942014773998274,
          -58.197070005529056,
          -58.447576896293654,
          -58.70128078389291,
          -58.958418390378796,
          -59.20524170909641,
          -59.44723399903469,
          -59.69388276513721,
          -59.931027810033974,
          -60.165977657778846,
          -60.4028858163006,
          -60.635923995332774,
          -60.86840049443835,
          -61.099011161298996,
          -61.325072857826285,
          -61.552572902852525,
          -61.78186442401753,
          -62.00610369182656,
          -62.22918669114481,
          -62.45120033636901,
          -62.66727576523948,
          -62.879589792410876,
          -63.08974891346408,
          -63.29184799188126,
          -63.486150043694316,
          -63.68212296761833,
          -63.86879288188045,
          -64.05406816514606,
          -64.24127952634656,
          -64.42679519785167,
          -64.60940060804988,
          -64.79549943956603,
          -64.97872401622303,
          -65.15444151049354,
          -65.32801925922261,
          -65.5010308641436,
          -65.6690807977606,
          -65.83598480396726,
          -66.00257711323798,
          -66.16103668846448,
          -66.31358773017325,
          -66.4655443820104,
          -66.61597280568952,
          -66.7633316363911,
          -66.9144278711085,
          -67.06458938311995,
          -67.20988754556,
          -67.35477514527832,
          -67.49798257352218,
          -67.6346399139633,
          -67.77105389797094,
          -67.90665128465112,
          -68.03823275845356,
          -68.16493582203498,
          -68.2896012594511,
          -68.41387172692838,
          -68.53705570690228,
          -68.65882461662041,
          -68.7799636896839,
          -68.90099820793556,
          -69.02059525215228,
          -69.13835116649797,
          -69.25683954163979,
          -69.37662718872424,
          -69.49376580699942,
          -69.61047033623086,
          -69.72717242719273,
          -69.84145886864682,
          -69.94982029032533,
          -70.05864851901192,
          -70.16732703621027,
          -70.27151727827419,
          -70.37548834154985,
          -70.48073257001012,
          -70.5829090979195,
          -70.68274677358421,
          -70.78443357946844,
          -70.88324425648482,
          -70.97875286639791,
          -71.0771372511972,
          -71.17400172032515,
          -71.26666261625638,
          -71.36021160708452,
          -71.45432636041001,
          -71.54492733949573,
          -71.63466489105116,
          -71.72399609523117,
          -71.81149568228606,
          -71.89823959411831,
          -71.98727468863211,
          -72.0758127803173,
          -72.16293437796791,
          -72.24940121128824,
          -72.33655908358352,
          -72.42154608291942,
          -72.50624690961207,
          -72.59123584654553,
          -72.67362123085358,
          -72.75186449679083,
          -72.82996198472189,
          -72.90490868215244,
          -72.97216599709894,
          -73.03504118983045,
          -73.09233370380218,
          -73.14451355979722,
          -73.1919683590342,
          -73.23528530488475,
          -73.27076059019343,
          -73.299488019885,
          -73.32362145007964,
          -73.33851140409004,
          -73.34531509384277,
          -73.34695945224483,
          -73.3424087915722,
          -73.32927881981134,
          -73.31226240646915,
          -73.2913679854743,
          -73.26556044980245,
          -73.23357381696566,
          -73.19316870617422,
          -73.14410981350582,
          -73.09015924720568,
          -73.02809580184176,
          -72.95659557025354,
          -72.8758583497977,
          -72.78872408487702,
          -72.68912027937967,
          -72.58337446465849,
          -72.46927066682753,
          -72.33150129817837,
          -72.18001428613026,
          -72.0243428194608,
          -71.84454500362263,
          -71.65815842349501,
          -71.49037568036576,
          -71.30876935098065,
          -71.11536600067517,
          -70.918510031055,
          -70.70831981370121,
          -70.48326402899058,
          -70.25481640942388,
          -70.0209624884734,
          -69.77772697405878,
          -69.52418182853609,
          -69.24642944281652,
          -68.96152470675838,
          -68.66849124212922,
          -68.36533051358055,
          -68.05095836453975,
          -67.72653230141428,
          -67.40800899464818,
          -67.07722682486768,
          -66.73974947011678,
          -66.39400293804786,
          -66.04112442409881,
          -65.68870114746116,
          -65.3252483383514,
          -64.9690263792324,
          -64.61522214180339,
          -64.25733066435907,
          -63.896024046542664,
          -63.54395670129856,
          -63.1810097778616,
          -62.81461679950509,
          -62.462797250069386,
          -62.105486920101235,
          -61.739157656934054,
          -61.371912575150866,
          -61.002145638833085,
          -60.62331255397244,
          -60.24365392961673,
          -59.86259983590844,
          -59.47781512744066,
          -59.096471828561725,
          -58.70280251911583,
          -58.303276871678776,
          -57.90745462998524,
          -57.504595142428485,
          -57.0966764523211,
          -56.69158748334247,
          -56.285752056943494,
          -55.87673676370104,
          -55.47318605198147,
          -55.06618157922572,
          -54.665725044789625,
          -54.26595706250994,
          -53.857825526175226,
          -53.454269450239025,
          -53.06013790782204,
          -52.65472789689884,
          -52.25882172385109,
          -51.87490334890676,
          -51.47517555816263,
          -51.090607751439016,
          -50.713532095332575,
          -50.322817204092026,
          -49.94353977548596,
          -49.56960416043476,
          -49.181510866065764,
          -48.80359830476866,
          -48.4448484297422,
          -48.062382789169405,
          -47.67769802278691,
          -47.31172074956801,
          -46.92809033117677,
          -46.538474389050236,
          -46.16966764647056,
          -45.793121883677884,
          -45.40924538838363,
          -45.03933168433307,
          -44.66302865712396,
          -44.27767986426334,
          -43.91017910195085,
          -43.548231782474964,
          -43.18426635421187,
          -42.83115000476785,
          -42.48264528557074,
          -42.14120091959226,
          -41.79415281047823,
          -41.448216382821734,
          -41.095658436095306,
          -40.74045215053444,
          -40.38941567630401,
          -40.030357553279735,
          -39.66004802795179,
          -39.28816934699813,
          -38.92008888138836,
          -38.53951639982919,
          -38.16579844170024,
          -37.80201826545343,
          -37.4316824132214,
          -37.07636853113231,
          -36.731254333408614,
          -36.36886406753462,
          -35.994593852746696,
          -35.644686155523374,
          -35.29275641245632,
          -34.9221115546295,
          -34.55673588553961,
          -34.20032882942233,
          -33.83728767472021,
          -33.45697811608634,
          -33.08519563632155,
          -32.728002369484535,
          -32.36119685971681,
          -31.977475412711723,
          -31.616290722678038,
          -31.251161151136085,
          -30.855887380410685,
          -30.47225987380637,
          -30.112296712085538,
          -29.735067792671984,
          -29.355465807928212,
          -29.01767533126146,
          -28.680667256120955,
          -28.31921822196352,
          -27.97768005804322,
          -27.64634110188014,
          -27.29371948580858,
          -26.955000168482044,
          -26.624163410977957,
          -26.288802749226107,
          -25.96300211141147,
          -25.644157811184783,
          -25.327056545952257,
          -25.027643932369575,
          -24.730564143525797,
          -24.441578575588572,
          -24.169146097405985,
          -23.895351187594173,
          -23.63028700949434,
          -23.38296078570461,
          -23.14604931948845,
          -22.916478434330745,
          -22.70735651481451,
          -22.514005728692524,
          -22.329998272855793,
          -22.171505652456872,
          -22.029889435845746,
          -21.894412725974114,
          -21.78228510233631,
          -21.68518470781308,
          -21.59812155651093,
          -21.526664627147596,
          -21.46860293568498,
          -21.420539513005977,
          -21.384150362160078,
          -21.360917704232072,
          -21.34954348239964,
          -21.347730488762924,
          -21.355580505067692,
          -21.372648608046457,
          -21.3978895192888,
          -21.43044603174177,
          -21.471452813977116,
          -21.520787475343546,
          -21.579112284658947,
          -21.64354971943037,
          -21.713874490410145,
          -21.79184470150812,
          -21.876986914490168,
          -21.96544535695405,
          -22.05611358331269,
          -22.156054009105308,
          -22.256593663555137,
          -22.357601166068722,
          -22.466490675010423,
          -22.577486612307805,
          -22.685844058486587,
          -22.800832239871397,
          -22.913894083257276,
          -23.02742504509644,
          -23.14686173528819,
          -23.265635507621756,
          -23.383383408534776,
          -23.506092238075524,
          -23.628263199794006,
          -23.746394027939324,
          -23.868957372851582,
          -23.988830886203996,
          -24.10567964078512,
          -24.22435960299237,
          -24.34058552757865,
          -24.452572459304545,
          -24.56388831150348,
          -24.674461733590807,
          -24.785902768653536,
          -24.895137988378217,
          -25.006350719277297,
          -25.11759056525727,
          -25.22791188299324,
          -25.337221370274982,
          -25.448966595733047,
          -25.562735125114518,
          -25.677846585016777,
          -25.79463943932319,
          -25.915713709840393,
          -26.05309114117935,
          -26.181002826989857,
          -26.31516199984558,
          -26.454617501708643,
          -26.596105223950445,
          -26.74490022057487,
          -26.89710439552725,
          -27.052115549729542,
          -27.21716863699173,
          -27.385546391576813,
          -27.5540481686624,
          -27.733667049908824,
          -27.915404422007466,
          -28.08703068348064,
          -28.268331385924668,
          -28.44997703764731,
          -28.623567168102102,
          -28.802148517620413,
          -28.98714174059946,
          -29.158786128981784,
          -29.33031276672451,
          -29.505906541512033,
          -29.674513162984464,
          -29.842594653558052,
          -30.018725428694076,
          -30.193115327473397,
          -30.36093531459758,
          -30.533288718119326,
          -30.7074120461382,
          -30.88242342936583,
          -31.056804731709143,
          -31.238054817841395,
          -31.41832962220704,
          -31.59600747980589,
          -31.77725005068032,
          -31.959089786116657,
          -32.13843940973086,
          -32.31692212486721,
          -32.49912140190639,
          -32.68094620894967,
          -32.85854325658454,
          -33.03843065730013,
          -33.220607826591774,
          -33.39433998624003,
          -33.56453442653805,
          -33.73328469536549,
          -33.89625837329445,
          -34.05685182777162,
          -34.21273828291849,
          -34.36079847525791,
          -34.50036662722723,
          -34.63451845931453,
          -34.76022089678012,
          -34.87757621300925,
          -34.995826049520176,
          -35.109700034739355,
          -35.217170967816976,
          -35.32522092774323,
          -35.42601635100748,
          -35.52081672573161,
          -35.61305180879768,
          -35.6960979698165,
          -35.77396957510407,
          -35.850287610540086,
          -35.92099082034511,
          -35.99055615817691,
          -36.06215681655589,
          -36.12625174757882,
          -36.19003801965097,
          -36.257201658343085,
          -36.31772119051593,
          -36.37925753930431,
          -36.44161303355463,
          -36.50001273721537,
          -36.55558580929922,
          -36.61388019442608,
          -36.66907481331578,
          -36.7201508134886,
          -36.771543375522924,
          -36.820361795533444,
          -36.8653732662636,
          -36.90904771130603,
          -36.950963689888844,
          -36.99143231778586,
          -37.032876369583775,
          -37.07395239415177,
          -37.116882095021914,
          -37.16277527765196,
          -37.21059543611934,
          -37.259212505421836,
          -37.30777624741638,
          -37.3580817430735,
          -37.408806823713284,
          -37.45939363954084,
          -37.51165032368335,
          -37.56745677446037,
          -37.62612219928459,
          -37.68473941635717,
          -37.74329437562592,
          -37.80139604481766,
          -37.85826472824297,
          -37.91558332731925,
          -37.975349226051364,
          -38.03435687639339,
          -38.09420449912109,
          -38.15508525727983,
          -38.21804998030959,
          -38.28161549201361,
          -38.348479589781206,
          -38.41707661278754,
          -38.48649857567124,
          -38.56022360068908,
          -38.636629483553854,
          -38.7135357334543,
          -38.805735547576035,
          -38.89794135909566,
          -38.992763532192456,
          -39.09235706618665,
          -39.198407158233756,
          -39.30397097995307,
          -39.41269334100938,
          -39.52769184278593,
          -39.640097203588674,
          -39.75180558087459,
          -39.870650344317774,
          -39.98884954358368,
          -40.1066709983397,
          -40.22838674105961,
          -40.3462994792553,
          -40.4691352147877,
          -40.5979271308363,
          -40.724106268875964,
          -40.85594362991394,
          -40.995353075372975,
          -41.134157015113836,
          -41.28127444889768,
          -41.44006024885091,
          -41.608035097763796,
          -41.78888625628457,
          -41.9748382738213,
          -42.16411434677769,
          -42.36535549935075,
          -42.57579816572816,
          -42.80049713766172,
          -43.02337075710654,
          -43.24689201724717,
          -43.497279433114976,
          -43.74603636513933,
          -43.98200479679747,
          -44.23040045138251,
          -44.485857650140844,
          -44.739184064761446,
          -44.997872630275744,
          -45.26070066858167,
          -45.523645603503546,
          -45.78847717037881,
          -46.04773110733275,
          -46.2992685722003,
          -46.55259145446595,
          -46.80007144209028,
          -47.03845237717201,
          -47.27045894331738,
          -47.4926324932838,
          -47.72366491521886,
          -47.923117693638396,
          -48.11535493101869,
          -48.29659317863487,
          -48.47009199345922,
          -48.637838119736,
          -48.79572843895207,
          -48.944495597548574,
          -49.08694433152678,
          -49.22090298307765,
          -49.34651754585118,
          -49.46533616941493,
          -49.5765442194328,
          -49.68364513813707,
          -49.78879809149675,
          -49.889262692400614,
          -49.9874158272796,
          -50.09634376092556,
          -50.19576710057528,
          -50.297358091270446,
          -50.40030751286942,
          -50.50512372765578,
          -50.61493278372968,
          -50.725778079211544,
          -50.83807633716309,
          -50.952604360629145,
          -51.069484093994326,
          -51.1914745656385,
          -51.31343961475373,
          -51.43767964447409,
          -51.568411580925336,
          -51.703359570426095,
          -51.838878158797286,
          -51.980465520918976,
          -52.12988377836994,
          -52.2787234498552,
          -52.433643418508495,
          -52.59124637272818,
          -52.75576543549834,
          -52.92723801656904,
          -53.09841357511194,
          -53.28096049895093,
          -53.47299187937339,
          -53.65979836561209,
          -53.85197386929605,
          -54.05830275954625,
          -54.26462258086851,
          -54.47298960068094,
          -54.69639809207101,
          -54.92165184926563,
          -55.140997397553726,
          -55.3682536213105,
          -55.62434382218987,
          -55.855937101434016,
          -56.088887631397164,
          -56.32682179904883,
          -56.56866772283272,
          -56.81154467589484,
          -57.052939783540054,
          -57.2970527772479,
          -57.54214075775572,
          -57.78669197780942,
          -58.032497304470176,
          -58.27967952359254,
          -58.52774357224673,
          -58.77324601619516,
          -59.019509838824206,
          -59.26156790685768,
          -59.496353226895316,
          -59.728490885098786,
          -59.96132338045377,
          -60.18548071028015,
          -60.40567806437624,
          -60.631134611711715,
          -60.85136762315885,
          -61.069033495158784,
          -61.289347958701384,
          -61.50736395700268,
          -61.72347449000393,
          -61.939433601832036,
          -62.158663735438424,
          -62.37831023797241,
          -62.589998805896094,
          -62.801589910631016,
          -63.01407203613896,
          -63.21925101967681,
          -63.420167343260886,
          -63.61693401032472,
          -63.801862417023145,
          -63.988055628833884,
          -64.17375911329682,
          -64.35002008589018,
          -64.5236144681962,
          -64.69821147686149,
          -64.8683362185876,
          -65.03690332883215,
          -65.20572564603471,
          -65.37083184703691,
          -65.5336935025303,
          -65.69478772717814,
          -65.85550151993193,
          -66.01141360499129,
          -66.16347518903787,
          -66.31600828851577,
          -66.46685912434538,
          -66.61327058465216,
          -66.75775482380826,
          -66.90273195606284,
          -67.0451210619066,
          -67.18581604536278,
          -67.32652949042996,
          -67.46236741218684,
          -67.59471377435128,
          -67.72909579005884,
          -67.85708759166262,
          -67.98331332316326,
          -68.10856359109131,
          -68.23196028232547,
          -68.35270906625568,
          -68.47234904104525,
          -68.58894775687868,
          -68.70519331366043,
          -68.81933775352118,
          -68.9287282967578,
          -69.0350238041871,
          -69.13931426185329,
          -69.24108634981746,
          -69.34074525673996,
          -69.43985139453707,
          -69.53891835664706,
          -69.63756927493108,
          -69.73643952069175,
          -69.835510543083,
          -69.93325376388403,
          -70.02713854660192,
          -70.12218653390872,
          -70.21863083959651,
          -70.31050182161633,
          -70.40344900670789,
          -70.49801069897822,
          -70.59049777649363,
          -70.68120128931315,
          -70.77460918967162,
          -70.86659526620204,
          -70.95608610167788,
          -71.04888932948845,
          -71.14220723778301,
          -71.2333036714523,
          -71.32667892572601,
          -71.42176601217464,
          -71.51345143520112,
          -71.6052065561612,
          -71.69851796318068,
          -71.79124783698138,
          -71.88443953462979,
          -71.98045729420745,
          -72.07651352764492,
          -72.17089185978968,
          -72.26771600686197,
          -72.36762094583482,
          -72.4662781235121,
          -72.56529152217168,
          -72.66201877693607,
          -72.75159279818001,
          -72.83639716468278,
          -72.91553209081161,
          -72.98838838000754,
          -73.05353020727999,
          -73.11455549438739,
          -73.1701273981084,
          -73.21761953976316,
          -73.26305864936852,
          -73.30208247936146,
          -73.33645770433473,
          -73.36328313632707,
          -73.38163615064862,
          -73.39005826457684,
          -73.3866503716562,
          -73.37400770830855,
          -73.35194307038122,
          -73.31649179531554,
          -73.27070148876368,
          -73.21394170131056,
          -73.15035019123178,
          -73.08311978347196,
          -73.00253306695204,
          -72.90854317889664,
          -72.8117280172042,
          -72.70427412025454,
          -72.5828492945219,
          -72.4596292587395,
          -72.32496285568756,
          -72.18089137001792,
          -72.03529966191883,
          -71.86587160094157,
          -71.68519964704127,
          -71.5060972856814,
          -71.30747012180845,
          -71.10345346077327,
          -70.90409173025043,
          -70.68989897080223,
          -70.46301300837499,
          -70.23453850822543,
          -69.99370391280686,
          -69.74306451517064,
          -69.4959556154675,
          -69.2394447764751,
          -68.96774231204915,
          -68.69006828212707,
          -68.40043206298986,
          -68.09948161268093,
          -67.79282386824059,
          -67.47152927350916,
          -67.14480627156297,
          -66.81698670152699,
          -66.48051217030299,
          -66.13570153059416,
          -65.78647079032615,
          -65.4305139246895,
          -65.07917736454287,
          -64.72365256364178,
          -64.35613278813504,
          -64.00350270732935,
          -63.655136203008,
          -63.28886564557143,
          -62.9273300654285,
          -62.579748916534875,
          -62.21017372899824,
          -61.836477619202384,
          -61.47350337887478,
          -61.1008249535478,
          -60.71415475534699,
          -60.332003420196386,
          -59.943172039128854,
          -59.5485529376962,
          -59.15426482353507,
          -58.755637214234206,
          -58.35944865007205,
          -57.96476758828307,
          -57.56247830460719,
          -57.161140157436456,
          -56.757150457204766,
          -56.34768032479303,
          -55.94168592092459,
          -55.53823042428493,
          -55.12830973725134,
          -54.72426812679187,
          -54.31949894213728,
          -53.90381736075342,
          -53.49621002591705,
          -53.0846398593366,
          -52.66291357533989,
          -52.25341797433776,
          -51.850147258909864,
          -51.43450981864474,
          -51.0365245660489,
          -50.639311770561314,
          -50.23593871875689,
          -49.84051448336762,
          -49.439048458325956,
          -49.035373660510835,
          -48.638461917228796,
          -48.23818514395617,
          -47.83466478803581,
          -47.45112056857801,
          -47.05763278466847,
          -46.65462077974918,
          -46.265031651687735,
          -45.8771526776741,
          -45.47841986714464,
          -45.092728007361636,
          -44.70829649211626,
          -44.31425058319479,
          -43.92707972096912,
          -43.53537566959353,
          -43.140793675114004,
          -42.75961674373031,
          -42.384060074633446,
          -42.01561279186344,
          -41.65556265907764,
          -41.2995770107581,
          -40.946812727407384,
          -40.59555163971216,
          -40.23539967134619,
          -39.83077264214173,
          -39.46922443327784,
          -39.10261505271557,
          -38.72285868011823,
          -38.34155409149054,
          -37.95830984399811,
          -37.57513454571789,
          -37.191304760479625,
          -36.81228982990092,
          -36.453848817041255,
          -36.10962661123027,
          -35.76992828774044,
          -35.43235562368165,
          -35.09771367660345,
          -34.761070274268704,
          -34.430830560281635,
          -34.064936749467876,
          -33.72802115042855,
          -33.3884745768605,
          -33.04053844542425,
          -32.67824290852522,
          -32.30606908525183,
          -31.949736176341432,
          -31.593263273275998,
          -31.21765403116339,
          -30.84924780909487,
          -30.49996112795178,
          -30.131494928893538,
          -29.75869173195225,
          -29.426153827602022,
          -29.09757429589814,
          -28.76331572748573,
          -28.4405905877889,
          -28.125292329920228,
          -27.8155872775575,
          -27.493448737626125,
          -27.174845519305034,
          -26.863668142690212,
          -26.539548198055,
          -26.208131612719583,
          -25.882742137279763,
          -25.560682506944286,
          -25.248144214210402,
          -24.94114367309649,
          -24.64343167338548,
          -24.362160350965954,
          -24.08613851774954,
          -23.817602907175132,
          -23.56744787616472,
          -23.356015671971146,
          -23.151980651712975,
          -22.95480771635995,
          -22.769441901460297,
          -22.597136903305817,
          -22.426157284335947,
          -22.27166366447541,
          -22.1324945742302,
          -22.00130698839695,
          -21.876265645220474,
          -21.75434285139997,
          -21.645254344648617,
          -21.547557005019296,
          -21.45856069978314,
          -21.37939293682077,
          -21.311189013530417,
          -21.25309551201301,
          -21.20557348792329,
          -21.171527159773515,
          -21.150957991194968,
          -21.14130200926466,
          -21.14025867458907,
          -21.147961798964047,
          -21.164197151549327,
          -21.18824462908672,
          -21.21966739881452,
          -21.261952053246265,
          -21.311996859093508,
          -21.366131815035523,
          -21.426038309354904,
          -21.495373934270177,
          -21.567955697698117,
          -21.644642539758348,
          -21.732794006910982,
          -21.820461877566785,
          -21.910900047123498,
          -22.011139657176635,
          -22.110251970269548,
          -22.207773884133747,
          -22.31299887627784,
          -22.414125583728794,
          -22.515190634189363,
          -22.62249533479528,
          -22.730541938980085,
          -22.838987962371448,
          -22.952646705541515,
          -23.06838414896128,
          -23.180429927557974,
          -23.296060714071494,
          -23.413192561394116,
          -23.529043078436736,
          -23.646830262371253,
          -23.76618527124554,
          -23.883010770436165,
          -23.998695889332346,
          -24.114510168247467,
          -24.229932321702456,
          -24.349513825273373,
          -24.46569754239584,
          -24.583037437367008,
          -24.69839248535096,
          -24.8125479296067,
          -24.924394357554746,
          -25.034280336750573,
          -25.146661463453228,
          -25.258615913407247,
          -25.370027944819448,
          -25.48201818696872,
          -25.594674485710865,
          -25.70855185414031,
          -25.825369750386947,
          -25.948013831457107,
          -26.074575968770056,
          -26.20187795843058,
          -26.3372241379381,
          -26.475654507637902,
          -26.613111328826246,
          -26.758472964173844,
          -26.909911565185983,
          -27.062880474483674,
          -27.223308590270733,
          -27.39709571678683,
          -27.56437525379657,
          -27.731090354296406,
          -27.909967760479717,
          -28.082592547246488,
          -28.256855683377623,
          -28.441568873274427,
          -28.62323793446386,
          -28.800517794148625,
          -28.97921707859944,
          -29.15763802650757,
          -29.32991328126194,
          -29.50635196611896,
          -29.683277368690934,
          -29.86152289239508,
          -30.034442351516546,
          -30.207041266426565,
          -30.38047756978916,
          -30.556496988681747,
          -30.731094175719168,
          -30.908611320169694,
          -31.09119761384564,
          -31.267628697179813,
          -31.44237864562472,
          -31.61648346992752,
          -31.79372627018451,
          -31.965404650868926,
          -32.1377182409115,
          -32.31234807631853,
          -32.48281031826397,
          -32.651604616090424,
          -32.821689646498704,
          -32.99251020534204,
          -33.15963768414815,
          -33.32681250036105,
          -33.4920865431513,
          -33.65085490929323,
          -33.81257237209739,
          -33.96919173036498,
          -34.11165882221215,
          -34.251662605275875,
          -34.383907141372084,
          -34.51014533806945,
          -34.63050273278304,
          -34.746729444854346,
          -34.859697273761114,
          -34.969802736821386,
          -35.07417576552302,
          -35.17476816452238,
          -35.27138688436677,
          -35.364899049192125,
          -35.453327789637434,
          -35.5328169499633,
          -35.609244510032724,
          -35.6826138209185,
          -35.74977862580279,
          -35.81500672838077,
          -35.88192158112244,
          -35.942921690403494,
          -36.002179587006516,
          -36.06609667012786,
          -36.12637253909442,
          -36.18345419230827,
          -36.24493760294374,
          -36.30529625873671,
          -36.364839077668876,
          -36.428505599417306,
          -36.49522661031054,
          -36.56363478847932,
          -36.63710760798189,
          -36.71123301780791,
          -36.78222335371588,
          -36.85195795002662,
          -36.91853852386554,
          -36.98234954054238,
          -37.04389356771069,
          -37.10499677065232,
          -37.16534516451735,
          -37.224170107050696,
          -37.28280200350135,
          -37.339885199625684,
          -37.39648174857182,
          -37.45148984848398,
          -37.50646642243688,
          -37.56071198436012,
          -37.61458021804285,
          -37.66885063614813,
          -37.72513253379038,
          -37.78412111826494,
          -37.844278895107536,
          -37.90277794206758,
          -37.96177968865448,
          -38.02038787557107,
          -38.075196790831605,
          -38.12855014990877,
          -38.18358897831821,
          -38.23237750887591,
          -38.281048678981826,
          -38.32973351622501,
          -38.37585017490633,
          -38.419831201724996,
          -38.461883479514555,
          -38.50248969525944,
          -38.54228972829945,
          -38.57974311447889,
          -38.61906683149036,
          -38.662987591884615,
          -38.708152160755645,
          -38.7538632966728,
          -38.80723895795233,
          -38.86394351500577,
          -38.92379686133418,
          -38.99444680855197,
          -39.06873158039537,
          -39.14372931978027,
          -39.22923763504379,
          -39.318160259924284,
          -39.40985085571478,
          -39.51275130065492,
          -39.61122438541254,
          -39.714470911702534,
          -39.8284911944118,
          -39.94158870101025,
          -40.06100659443418,
          -40.19435475796122,
          -40.33186039164071,
          -40.47682463618865,
          -40.633597056362724,
          -40.79695911625718,
          -40.968220849515,
          -41.15403227418905,
          -41.35153141315813,
          -41.55781594961092,
          -41.77531954575916,
          -42.00420403549024,
          -42.247393582151105,
          -42.50156310109564,
          -42.76156242322968,
          -43.03445494217945,
          -43.31517011160254,
          -43.59347004207036,
          -43.88930962336479,
          -44.18794412627615,
          -44.48608944446388,
          -44.78889267724565,
          -45.089537159473515,
          -45.38698177120378,
          -45.682403627769865,
          -45.97529097931601,
          -46.261430098627095,
          -46.53526208599471,
          -46.80630225030792,
          -47.06785442598212,
          -47.3152266334425,
          -47.55148647420521,
          -47.7727859855664,
          -47.979927906250204,
          -48.17807357325699,
          -48.36401955571604,
          -48.535696073243024,
          -48.698161843699104,
          -48.866119315437736,
          -49.007279536280805,
          -49.142422169914305,
          -49.27158570672841,
          -49.39432867880314,
          -49.51154581961109,
          -49.622143228463365,
          -49.72858427761303,
          -49.83137919900098,
          -49.930705866692385,
          -50.02878875156228,
          -50.125757551113885,
          -50.22244616789082,
          -50.3191528476129,
          -50.41726936908804,
          -50.51881736102967,
          -50.62161135459325,
          -50.725926855578386,
          -51.104104140815814,
          -51.22722230732899,
          -51.35859689132128,
          -51.497454856501264,
          -51.64049622582717,
          -51.7908697346413,
          -51.94977633626489,
          -52.110707221040876,
          -52.27606294113724,
          -52.446041568212955,
          -52.62682281192127,
          -52.81087641960585,
          -52.99751965688172,
          -53.20069328308993,
          -53.40593530267518,
          -53.60576161773223,
          -53.81662011621015,
          -54.0363859903432,
          -54.24895745990442,
          -54.470291911878576,
          -54.702035372537516,
          -54.926283360310514,
          -55.153412288459734,
          -55.38859946280714,
          -55.62136929201882,
          -55.85464556458957,
          -56.09361780526448,
          -56.33891086598978,
          -56.585375250091275,
          -56.832455481140336,
          -57.08339681330611,
          -57.335510781256005,
          -57.58576096869138,
          -57.83955120557427,
          -58.09600277330934,
          -58.352361145455035,
          -58.60888287383229,
          -58.867941412667015,
          -59.12192676004352,
          -59.37101674191034,
          -59.62012198677071,
          -59.86747564315497,
          -60.10659450424401,
          -60.34725169686158,
          -60.59143425121999,
          -60.826934719278476,
          -61.064590497045124,
          -61.30420734228774,
          -61.53964230085126,
          -61.771863926087114,
          -62.00771278686136,
          -62.24277486200863,
          -62.46852697600483,
          -62.69539498731651,
          -62.921773392318904,
          -63.13995199077138,
          -63.353377089943685,
          -63.558165939789085,
          -63.75233187361694,
          -63.94798892266304,
          -64.13748826811339,
          -64.3209118127535,
          -64.50594654125743,
          -64.68832685466805,
          -64.86769665506284,
          -65.04781813965363,
          -65.22564273730137,
          -65.39978413217911,
          -65.57328278158236,
          -65.74517774677835,
          -65.90903561375244,
          -66.07151149511637,
          -66.23364536307122,
          -66.39001437685894,
          -66.54268316367983,
          -66.69482035322696,
          -66.84299493688042,
          -66.98274034898887,
          -67.11686109685202,
          -67.2473232768979,
          -67.37275471986435,
          -67.49853608468358,
          -67.63057259800027,
          -67.74723486022438,
          -67.8627077497535,
          -67.9754571031743,
          -68.08563069929107,
          -68.19746510360383,
          -68.30848435778216,
          -68.41775607238436,
          -68.52744413690742,
          -68.633129533093,
          -68.73462688784191,
          -68.83376460339574,
          -68.92985064092387,
          -69.02481244365634,
          -69.1173943163264,
          -69.20688750904361,
          -69.29468845144093,
          -69.38250890651003,
          -69.47103973688623,
          -69.55929183473162,
          -69.64702136147605,
          -69.73280545630337,
          -69.81785841424487,
          -69.90491359660227,
          -69.99002561248199,
          -70.07270331667695,
          -70.15718528968421,
          -70.24114478170252,
          -70.32285413442807,
          -70.40286431587688,
          -70.48500864897936,
          -70.56735820100766,
          -70.64829401426988,
          -70.73064782133481,
          -70.81531743197613,
          -70.90159992571424,
          -70.99074831706196,
          -71.08203625302541,
          -71.1737823807634,
          -71.26560347411566,
          -71.35571460623784,
          -71.44458409917311,
          -71.53410019676936,
          -71.62295534525737,
          -71.7111769274895,
          -71.80043232083361,
          -71.89071528860671,
          -71.97862287266754,
          -72.06534242553148,
          -72.15351705548409,
          -72.24117369948681,
          -72.32650167517815,
          -72.41122097304289,
          -72.49328193817811,
          -72.57072266807357,
          -72.64345901658709,
          -72.71068551852751,
          -72.77265378086943,
          -72.83047258330451,
          -72.88209913081309,
          -72.92911119174103,
          -72.97024557292157,
          -73.0053868767717,
          -73.0383985314366,
          -73.06545461102495,
          -73.0852370553975,
          -73.09928378783825,
          -73.1087244585547,
          -73.11147575647097,
          -73.10607968738555,
          -73.0951326101401,
          -73.07672976892772,
          -73.04882031546873,
          -73.0153053370118,
          -72.9738471882484,
          -72.92611455391813,
          -72.87199505469133,
          -72.80457282100957,
          -72.73097061433972,
          -72.65216854718145,
          -72.56090098688745,
          -72.46202221143442,
          -72.35736852543373,
          -72.23959141650906,
          -72.11878320863434,
          -71.9872752962235,
          -71.83335570725413,
          -71.67600007722505,
          -71.5082009586617,
          -71.3226854473823,
          -71.13967185499301,
          -70.95531392522747,
          -70.75511956253877,
          -70.54824546667773,
          -70.33577210613676,
          -70.10360904416274,
          -69.8636953328458,
          -69.62389018932022,
          -69.37241409173863,
          -69.11186569568176,
          -68.84310024975234,
          -68.56326051952144,
          -68.2788475443871,
          -67.98568182237305,
          -67.68116684124008,
          -67.37032745691873,
          -67.05976567889473,
          -66.73941471965175,
          -66.41002122166618,
          -66.07466277720971,
          -65.73825608816385,
          -65.40428778136757,
          -65.06069040998966,
          -64.71283201352946,
          -64.38068598184057,
          -64.04711991252417,
          -63.69919072118485,
          -63.36045179508659,
          -63.03081307576595,
          -62.68012909007039,
          -62.32914207032507,
          -61.989412403740566,
          -61.637577939691624,
          -61.274648871301345,
          -60.918499374464,
          -60.554813837407,
          -60.18255952722983,
          -59.814131800365786,
          -59.44028335958801,
          -59.066652406202465,
          -58.699669500159914,
          -58.32747429279155,
          -57.95035782823271,
          -57.57893243124308,
          -57.2015442561234,
          -56.82194501661254,
          -56.444909701417465,
          -56.07030598180746,
          -55.69193783730353,
          -55.320991664748064,
          -54.94326555580486,
          -54.565853351401366,
          -54.19275388213334,
          -53.80979434614635,
          -53.42879887286961,
          -53.056674984054744,
          -52.68218507457872,
          -52.30282238250406,
          -51.945454525362926,
          -51.57771802373846,
          -51.20765486741763,
          -50.8522112158168,
          -50.48447880841819,
          -50.1120619303601,
          -49.752072825817976,
          -49.38694215549192,
          -49.015260622606014,
          -48.652537033453896,
          -48.301659566727885,
          -47.93622987317094,
          -47.5723193998465,
          -47.21515073392902,
          -46.85766357491683,
          -46.49537288254257,
          -46.14264890857052,
          -45.79243412342383,
          -45.43645386527342,
          -45.085052382305506,
          -44.73595334042792,
          -44.379767622031174,
          -44.028763042692674,
          -43.685164444857925,
          -43.343848401608,
          -43.012091961379625,
          -42.69060782612624,
          -42.36425244115255,
          -42.04825224996773,
          -41.73480724870234,
          -41.41441243507075,
          -41.0921312480419,
          -40.76485267464405,
          -40.44072650062485,
          -40.11282446283272,
          -39.7736541006895,
          -39.42821715886703,
          -39.07752717892047,
          -38.72405253756792,
          -38.37030778842886,
          -38.01542125747221,
          -37.65771833034179,
          -37.30912094736801,
          -36.97015089642019,
          -36.62917551896926,
          -36.286347071222515,
          -35.94195532420182,
          -35.60710138784223,
          -35.26868239734169,
          -34.92113480034112,
          -34.57375815483517,
          -34.222897939554244,
          -33.877839771189244,
          -33.5152299650239,
          -33.15177753168167,
          -32.79719870871715,
          -32.43859434101738,
          -32.06062449476858,
          -31.6976841775139,
          -31.344135662429256,
          -30.96425179459354,
          -30.586699789811345,
          -30.23517487586146,
          -29.87593242086572,
          -29.508515417656383,
          -29.173218552870345,
          -28.85248231542016,
          -28.502487471058757,
          -28.15436597505832,
          -27.82600105176375,
          -27.480492381027922,
          -27.14040098056358,
          -26.818235037510153,
          -26.48786770164433,
          -26.168594017144397,
          -25.855947760439268,
          -25.543205646099622,
          -25.24361924081397,
          -24.958346399129535,
          -24.675161495617857,
          -24.405523781770352,
          -24.147787478236896,
          -23.882518986274178,
          -23.625294806610068,
          -23.38517342263037,
          -23.152766348575657,
          -22.926984042363703,
          -22.71657230599161,
          -22.52244116998466,
          -22.338667653741318,
          -22.178302880267452,
          -22.03615085465187,
          -21.904981151443053,
          -21.78990010064519,
          -21.6963480793184,
          -21.613747592994223,
          -21.54364303104233,
          -21.489888101017385,
          -21.449162135376433,
          -21.420155343571256,
          -21.404812291255986,
          -21.40213329016019,
          -21.410364979733004,
          -21.426419901066044,
          -21.450392900374975,
          -21.48255379374399,
          -21.52181980838533,
          -21.566752356307656,
          -21.617906400593903,
          -21.675744574721357,
          -21.74009389863133,
          -21.808948837752926,
          -21.881695033221146,
          -21.95996610249677,
          -22.043234161006392,
          -22.12873334291695,
          -22.216131199334185,
          -22.312097411132406,
          -22.40773944947401,
          -22.503296470655233,
          -22.604860789459906,
          -22.70734042294508,
          -22.806527681647584,
          -22.910816627161694,
          -23.014358524896686,
          -23.11652643527728,
          -23.224677322919145,
          -23.341089481025154,
          -23.460994431856744,
          -23.586267115755597,
          -23.71340177789751,
          -23.83760832125027,
          -23.96347255600051,
          -24.091878684772656,
          -24.217255789373564,
          -24.343818347883307,
          -24.472411613524987,
          -24.59255368192226,
          -24.707446420951598,
          -24.822001529025115,
          -24.936338059234696,
          -25.05346619487281,
          -25.168532093608093,
          -25.284772150448276,
          -25.399863934689044,
          -25.512926965641253,
          -25.623795242374193,
          -25.73869243665912,
          -25.8589866064603,
          -25.980525096739612,
          -26.10325281833032,
          -26.230922253086067,
          -26.36083833319771,
          -26.494724704125975,
          -26.632181265085112,
          -26.775610582136455,
          -26.920690184971154,
          -27.06160750835324,
          -27.205520303705732,
          -27.348691431134522,
          -27.492973293355632,
          -27.646363384845003,
          -27.80307212819232,
          -27.960243606801313,
          -28.12738507107007,
          -28.300127591950236,
          -28.462697404409184,
          -28.616130898816355,
          -28.764101486603447,
          -28.903455225751628,
          -29.047105846118832,
          -29.197672432922435,
          -29.340093284795767,
          -29.480170953913447,
          -29.626435268751734,
          -29.768619712304925,
          -29.907694450155788,
          -30.063491616359183,
          -30.2264148861466,
          -30.391165525726823,
          -30.551426562065945,
          -30.71109749627567,
          -30.872512599777036,
          -31.03737624842146,
          -31.198026544621342,
          -31.35786466378723,
          -31.52571873691776,
          -31.684402155851675,
          -31.838102843849853,
          -31.99288658025006,
          -32.1496604126573,
          -32.30598904381027,
          -32.45968877410026,
          -32.61603854432724,
          -32.76791095037131,
          -32.919650626058015,
          -33.06765874423673,
          -33.2178597785099,
          -33.365596639245545,
          -33.50724207131844,
          -33.6484933976596,
          -33.782886269933776,
          -33.912713808330366,
          -34.04134101986095,
          -34.161454401007475,
          -34.27607778327195,
          -34.38921456369967,
          -34.49702669521139,
          -34.6041454533932,
          -34.71258653644202,
          -34.81814139191315,
          -34.92442156617737,
          -35.03216765565739,
          -35.13733824058586,
          -35.24200591057709,
          -35.34633163784157,
          -35.44501160020167,
          -35.53957133994688,
          -35.63592727341846,
          -35.724942728733325,
          -35.81039933839135,
          -35.89608018183842,
          -35.983055487875625,
          -36.060055258248404,
          -36.13729389360015,
          -36.2190335217945,
          -36.29380199754092,
          -36.370085172867455,
          -36.448152006644364,
          -36.520831158203706,
          -36.59100718893863,
          -36.66216444260028,
          -36.73423179336943,
          -36.80433656535305,
          -36.87618225739581,
          -36.94537952166152,
          -37.010679968574514,
          -37.072969154176,
          -37.13285029859125,
          -37.191295790064,
          -37.25092507617021,
          -37.31183414492856,
          -37.3713380132829,
          -37.433365792362764,
          -37.4971670191308,
          -37.5628269128984,
          -37.63097813777338,
          -37.699012704893015,
          -37.769435757172225,
          -37.84189825486961,
          -37.914756035992724,
          -37.988742200839646,
          -38.06551436234993,
          -38.14708283579221,
          -38.22911926432711,
          -38.30904482859451,
          -38.3902750587055,
          -38.47160773935936,
          -38.550120030785145,
          -38.627287314663164,
          -38.70955147292591,
          -38.78572465026189,
          -38.86154282958575,
          -38.9382615457867,
          -39.00948838112435,
          -39.081504051841044,
          -39.15511425591152,
          -39.22727900136679,
          -39.29846265937135,
          -39.36872293272774,
          -39.438970452184016,
          -39.51232499659036,
          -39.588437810121455,
          -39.66396416195027,
          -39.743988370059036,
          -39.823112536793204,
          -39.90268698328979,
          -39.9867816678149,
          -40.072107999887486,
          -40.159006006417734,
          -40.250078036371875,
          -40.34362239027905,
          -40.43851925498407,
          -40.537980841227835,
          -40.63686774097731,
          -40.73795543783005,
          -40.844981139273216,
          -40.951997655991065,
          -41.062690713572,
          -41.18180314080349,
          -41.307329208067905,
          -41.44024518833797,
          -41.58153772520447,
          -41.733041062909344,
          -41.89537060354485,
          -42.07029808011077,
          -42.25720454661528,
          -42.45745057649343,
          -42.671435256628,
          -42.892956458648165,
          -43.13191280487126,
          -43.389287638409286,
          -43.65070052288813,
          -43.91365502178964,
          -44.19959321805714,
          -44.49737192850483,
          -44.79033843281663,
          -45.09598334134922,
          -45.405067274308934,
          -45.70920220166909,
          -46.01425072261265,
          -46.317304105233,
          -46.613317919410036,
          -46.89837567953706,
          -47.179077156090514,
          -47.45091126839585,
          -47.70893069272744,
          -47.95662111698227,
          -48.18789324522698,
          -48.405751102902144,
          -48.61268120552227,
          -48.80753421101286,
          -48.987618755372026,
          -49.1562446018585,
          -49.31277179685632,
          -49.457034962429695,
          -49.591081371629585,
          -49.71484328687455,
          -49.8304950212542,
          -49.93881467203453,
          -50.03962474813927,
          -50.13723889288927,
          -50.23107991068973,
          -50.320494546372174,
          -50.408648561633775,
          -50.497625457993195,
          -50.58806231571165,
          -50.68198472484677,
          -50.79033761795886,
          -50.89499511994884,
          -51.00324592740218,
          -51.115030614156616,
          -51.23129294714832,
          -51.35322385256986,
          -51.481471340784694,
          -51.61424372173705,
          -51.75393805702607,
          -51.90377061741117,
          -52.06050420202254,
          -52.222156271705295,
          -52.394580496612235,
          -52.57149118435109,
          -52.75292957732888,
          -52.9377989091786,
          -53.134282737481975,
          -53.33335510585575,
          -53.53409937865804,
          -53.753196876631485,
          -53.97381604718522,
          -54.18828048480063,
          -54.41403487900981,
          -54.64806054950085,
          -54.875146016140285,
          -55.113852348529534,
          -55.35932450445642,
          -55.59736520126808,
          -55.84171882926131,
          -56.0913281623881,
          -56.33675122268888,
          -56.586828509734204,
          -56.84645158231835,
          -57.105353229431735,
          -57.36315396310824,
          -57.62805759933618,
          -57.89511300182526,
          -58.15814254705349,
          -58.42489083303824,
          -58.69760737542457,
          -58.96942418517086,
          -59.24165393872915,
          -59.51799607437879,
          -59.78745639577197,
          -60.051496890101284,
          -60.318086325924355,
          -60.57647712497823,
          -60.829664493707966,
          -61.089348444484514,
          -61.342362295883774,
          -61.590171930938006,
          -61.840577862365556,
          -62.08899124020301,
          -62.32866134735973,
          -62.56948967078802,
          -62.810940186372875,
          -63.04181238803805,
          -63.270961800570134,
          -63.52118008974367,
          -63.73858861593142,
          -63.9522525364015,
          -64.15714907441796,
          -64.35680510475528,
          -64.55344204506143,
          -64.7450186534997,
          -64.93492156360699,
          -65.12505449436121,
          -65.30984675137664,
          -65.49602432660923,
          -65.68185049036664,
          -65.85909398972477,
          -66.03222030475257,
          -66.2064532389386,
          -66.37401886460268,
          -66.53539869670644,
          -66.6985382415549,
          -66.857341670653,
          -67.00712940751521,
          -67.15573684701633,
          -67.30613178967323,
          -67.45020065289773,
          -67.59357998259453,
          -67.73453120723646,
          -67.86918594435251,
          -68.0011948422586,
          -68.13257348039454,
          -68.25935694699257,
          -68.38566652761453,
          -68.51056179429035,
          -68.63436200715414,
          -68.75565096024698,
          -68.87546292780858,
          -68.99282874008783,
          -69.11023820445519,
          -69.22466758983161,
          -69.33468198051443,
          -69.44310951160371,
          -69.54881493634024,
          -69.65342167514686,
          -69.75714370448921,
          -69.8605528093441,
          -69.96358955871048,
          -70.06705091748779,
          -70.17159199691042,
          -70.27653473081132,
          -70.38163126501072,
          -70.48469938809419,
          -70.58894280010354,
          -70.6952027796743,
          -70.80683967692613,
          -70.90696307173944,
          -71.00849527404763,
          -71.10734642399387,
          -71.20210867594348,
          -71.29832012644825,
          -71.39494324686648,
          -71.48811737299084,
          -71.58071228282576,
          -71.67378359830272,
          -71.76504382257333,
          -71.85638880146503,
          -71.94775855297245,
          -72.03750961353443,
          -72.12567968732866,
          -72.21206477269702,
          -72.29753395289379,
          -72.38342029434568,
          -72.46731971505908,
          -72.5515910213241,
          -72.64663355544188,
          -72.732839311115,
          -72.81624316602283,
          -72.901715811989,
          -72.98705115780574,
          -73.07009560253982,
          -73.15129387580456,
          -73.22998566881122,
          -73.30417297342126,
          -73.37406424879377,
          -73.43827279790231,
          -73.49806968063889,
          -73.5521308174943,
          -73.60012315712991,
          -73.64249681469272,
          -73.67776486988559,
          -73.70786129595258,
          -73.73245491818513,
          -73.75037626017347,
          -73.76096310499868,
          -73.76761645811072,
          -73.76765015357171,
          -73.75765566842436,
          -73.74072933909764,
          -73.71620342746488,
          -73.68093604015272,
          -73.63982579510566,
          -73.59035007510316,
          -73.53466103521208,
          -73.47265353218445,
          -73.40309255384136,
          -73.32944400762746,
          -73.25130573791414,
          -73.16230480886657,
          -73.06752573671588,
          -72.9672829983631,
          -72.85611241352224,
          -72.74419859281247,
          -72.61921903993031,
          -72.47404739316538,
          -72.32686216697094,
          -72.16467187993177,
          -71.9885379108041,
          -71.81780401831426,
          -71.64248681967499,
          -71.45144925311202,
          -71.25363328925569,
          -71.05082778228895,
          -70.82933891285678,
          -70.60145680780992,
          -70.36555620250806,
          -70.11914779332301,
          -69.86427258962065,
          -69.60176588158231,
          -69.32821624436541,
          -69.04867461769744,
          -68.7622866254037,
          -68.46035136398608,
          -68.15417838541254,
          -67.84934334267064,
          -67.51660686204437,
          -67.18006026928688,
          -66.84683050956784,
          -66.5139525084509,
          -66.18958612057345,
          -65.86508625350565,
          -65.52600748979158,
          -65.19780033000949,
          -64.87306228785998,
          -64.53885253412979,
          -64.21174275802292,
          -63.889297093666265,
          -63.56603406039059,
          -63.22680774639339,
          -62.88925307727907,
          -62.55158389158242,
          -62.204757205436614,
          -61.850141228831596,
          -61.49493611992698,
          -61.133561501780655,
          -60.7682341474149,
          -60.403196154833125,
          -60.03311148041931,
          -59.66151870048452,
          -59.294543079513154,
          -58.92252380011841,
          -58.54585870532376,
          -58.17075925244724,
          -57.78989628918336,
          -57.40416890949777,
          -57.01767620400345,
          -56.63055227967966,
          -56.2398902039165,
          -55.815056094274745,
          -55.42416406330756,
          -55.037800670356056,
          -54.65814333611411,
          -54.27572995893224,
          -53.90526799348135,
          -53.54884526792905,
          -53.1904069727871,
          -52.83869899765796,
          -52.51539821997287,
          -52.18397723536897,
          -51.85326286316791,
          -51.54369886767894,
          -51.22154895006788,
          -50.8900600594513,
          -50.567919830073016,
          -50.238946547903275,
          -49.90651232739457,
          -49.57197917342724,
          -49.23157240598229,
          -48.89862461994845,
          -48.561948865908484,
          -48.2088730452881,
          -47.86152172391734,
          -47.515635822188536,
          -47.158799882982365,
          -46.80377744315119,
          -46.45426898482567,
          -46.09410455978452,
          -45.729982580655594,
          -45.373113659034374,
          -45.00680731941585,
          -44.63455124099906,
          -44.273173006355385,
          -43.91276741964215,
          -43.5533060258781,
          -43.207836711125424,
          -42.859755450366194,
          -42.515026160370205,
          -42.174556283897594,
          -41.827228888305825,
          -41.474203211374444,
          -41.1166003228051,
          -40.76126631629593,
          -40.39787635296161,
          -40.02305115063716,
          -39.64332177524524,
          -39.26138377887114,
          -38.87490905469687,
          -38.48941234249474,
          -38.10312517420079,
          -37.72321208719548,
          -37.35458157673017,
          -36.98509227572977,
          -36.61337380348764,
          -36.24343138388839,
          -35.88565943938279,
          -35.51894090174665,
          -35.14486172996532,
          -34.77690100262629,
          -34.413139594164754,
          -34.04020123593851,
          -33.65875654838488,
          -33.294072335597114,
          -32.9430046897531,
          -32.57604697232716,
          -32.21957629982182,
          -31.89288716544579,
          -31.548315725412877,
          -31.191063175333376,
          -30.855126303307152,
          -30.526094463741856,
          -30.190168716530895,
          -29.853459583523566,
          -29.537033855191776,
          -29.234367169527925,
          -28.912386761556956,
          -28.589913428867064,
          -28.28365768842951,
          -27.96768317526559,
          -27.646121184402677,
          -27.33720040958477,
          -27.021651497423683,
          -26.709951528558385,
          -26.408690283330845,
          -26.10660710189547,
          -25.806030843244482,
          -25.52021273064992,
          -25.238077132963465,
          -24.960202361192145,
          -24.702441811898723,
          -24.44206910812618,
          -24.178438374884472,
          -23.932752796138534,
          -23.697957088673878,
          -23.468088363313232,
          -23.24676333327689,
          -23.041116256445584,
          -22.847627037706772,
          -22.66558015740162,
          -22.506780926503883,
          -22.36131253966572,
          -22.223154946736862,
          -22.106767204562416,
          -22.0055917946128,
          -21.913345280482684,
          -21.83688567789569,
          -21.774353449959808,
          -21.725099594685577,
          -21.688985323927486,
          -21.66779355513553,
          -21.66030608881035,
          -21.664788800881023,
          -21.67989884857852,
          -21.70499464686902,
          -21.741247610544526,
          -21.78754799980009,
          -21.842325973360637,
          -21.905107015268626,
          -21.974332876644127,
          -22.05136276264909,
          -22.133163676920763,
          -22.218371266576543,
          -22.310521558986576,
          -22.40860015534457,
          -22.508613126915478,
          -22.609289371038862,
          -22.71382496821083,
          -22.820691050549115,
          -22.924692204138633,
          -23.03230104429842,
          -23.14383462442385,
          -23.250388408083037,
          -23.36118182242375,
          -23.473403513505087,
          -23.581556433942954,
          -23.694475229182572,
          -23.811210912908113,
          -23.92505655536757,
          -24.042729277753185,
          -24.162580327007138,
          -24.27982814133648,
          -24.39577483064936,
          -24.515711527890677,
          -24.632166887095853,
          -24.74770785086778,
          -24.8657160960641,
          -24.98031543136073,
          -25.09232632962804,
          -25.204551367529355,
          -25.31538009348689,
          -25.428093000116814,
          -25.541802724850776,
          -25.653470278878302,
          -25.768725268624824,
          -25.883854715918872,
          -25.99887929067349,
          -26.11332680776609,
          -26.230185343128916,
          -26.348394244416827,
          -26.467038324614,
          -26.587056173289348,
          -26.707141726174534,
          -26.82839831459594,
          -26.95172480503895,
          -27.088632898654566,
          -27.213282215996067,
          -27.330318260786278,
          -27.448982591299654,
          -27.56962666398281,
          -27.688239511316485,
          -27.810714016146456,
          -27.938183897315056,
          -28.0650872093922,
          -28.194880683342525,
          -28.333138671150422,
          -28.475966850131677,
          -28.61760821654979,
          -28.766071865948344,
          -28.92146894633009,
          -29.070657143446724,
          -29.22422802710299,
          -29.385903743844,
          -29.542416803210983,
          -29.695852358968107,
          -29.851503536036773,
          -30.006195950637736,
          -30.14856336818705,
          -30.29493053515212,
          -30.440294285828557,
          -30.587000217327315,
          -30.733322646456728,
          -30.874674696407837,
          -31.01731820512761,
          -31.16316280922664,
          -31.310119044395524,
          -31.45344521173325,
          -31.60767394929439,
          -31.766191557101273,
          -31.9190058298071,
          -32.074065503801485,
          -32.228796949286945,
          -32.383772776022994,
          -32.5410936792175,
          -32.694536222334115,
          -32.851903567622585,
          -33.00731397936124,
          -33.16479337679203,
          -33.32195672400879,
          -33.47817753691862,
          -33.63713624301213,
          -33.792569634726775,
          -33.94731391188095,
          -34.10329075153213,
          -34.25523369853277,
          -34.4079274320869,
          -34.563498765133495,
          -34.710589537913776,
          -34.85589298973087,
          -34.99914611466545,
          -35.134036033510604,
          -35.26538876619463,
          -35.38957006750351,
          -35.51121304820496,
          -35.62984354445944,
          -35.74184630850491,
          -35.85021819893029,
          -35.952990467030794,
          -36.04783564474804,
          -36.139501935712616,
          -36.224341487478966,
          -36.29999616730834,
          -36.372695122010256,
          -36.441052538782095,
          -36.50292336374147,
          -36.56620817451979,
          -36.63060500154476,
          -36.69127603050018,
          -36.75586038320107,
          -36.82216151579864,
          -36.881812676850565,
          -36.943891287636845,
          -37.00580343667554,
          -37.064972200238124,
          -37.12419393029799,
          -37.1856362431639,
          -37.24440312907708,
          -37.30370876832406,
          -37.36946333548556,
          -37.424478513873204,
          -37.476130524066555,
          -37.52683398474871,
          -37.575959487269806,
          -37.625142517126186,
          -37.67848777970751,
          -37.73327083379501,
          -37.79135549615383,
          -37.853619553999316,
          -37.91933421108968,
          -37.98769305223514,
          -38.05902781617655,
          -38.13467257549317,
          -38.212624414565816,
          -38.291838341694465,
          -38.372991048118166,
          -38.4570755685649,
          -38.54310598807688,
          -38.629521157064566,
          -38.71859799931532,
          -38.80453428000226,
          -38.88889156320609,
          -38.973395340598174,
          -39.055845926745334,
          -39.13535263929575,
          -39.216446102612764,
          -39.30030859574843,
          -39.380351751541,
          -39.45943892893928,
          -39.53727213526203,
          -39.61341596272377,
          -39.68764591577625,
          -39.75839456183066,
          -39.82889039671367,
          -39.89887000731089,
          -39.96780342280601,
          -40.03261238511189,
          -40.0975086193935,
          -40.15847314672556,
          -40.21613056346378,
          -40.27571688804471,
          -40.33631782904814,
          -40.393772456831634,
          -40.45105878171714,
          -40.51398034732638,
          -40.57636941356571,
          -40.63809129414276,
          -40.706375294108355,
          -40.77964353975551,
          -40.85774952271849,
          -40.94325778825428,
          -41.030378145817686,
          -41.123030717826204,
          -41.22530365075202,
          -41.33341408708455,
          -41.447538674650104,
          -41.57029218848021,
          -41.69767799045506,
          -41.831609278564535,
          -41.977255124425824,
          -42.13276642953561,
          -42.303686612216886,
          -42.489307909538404,
          -42.68536348100295,
          -42.89533021608527,
          -43.12239409554427,
          -43.36163292358729,
          -43.61071729634861,
          -43.87507741773644,
          -44.15899577150894,
          -44.44551025073052,
          -44.73572194980638,
          -45.037476230017006,
          -45.33434133482656,
          -45.63375539861817,
          -45.934273611890994,
          -46.2246161097934,
          -46.51860376423774,
          -46.80304120799316,
          -47.07243959361878,
          -47.34073115611892,
          -47.604272940148654,
          -47.848343341458154,
          -48.080532690116016,
          -48.30452853349216,
          -48.51264112400717,
          -48.70902912561279,
          -48.896694172169674,
          -49.07109008140121,
          -49.23493477866019,
          -49.389386429441714,
          -49.531356440876905,
          -49.66401278069163,
          -49.78790789402918,
          -49.90500911811212,
          -50.01555925926447,
          -50.11974526865521,
          -50.22069451438372,
          -50.31976315461191,
          -50.41499710680453,
          -50.50820149524243,
          -50.60233865674474,
          -50.69773349991716,
          -50.79430275689069,
          -50.8932559150181,
          -50.9982434665074,
          -51.107256735857966,
          -51.220208095445265,
          -51.34011509805129,
          -51.464285678518024,
          -51.59522568841392,
          -51.7312715779073,
          -51.87296321622957,
          -52.02557375764567,
          -52.18664529993934,
          -52.353214305233365,
          -52.5320650111789,
          -52.71479653015089,
          -52.89777777504159,
          -53.08470440195738,
          -53.28374009135521,
          -53.48716125101572,
          -53.68998017573295,
          -53.91000322667469,
          -54.13533458543162,
          -54.35342060705394,
          -54.58099670350793,
          -54.821927119247604,
          -55.05372578752008,
          -55.29206620718725,
          -55.540477380525786,
          -55.780943383535224,
          -56.0232542784252,
          -56.27384792825905,
          -56.519203875280624,
          -56.76662136797318,
          -57.020413642514974,
          -57.27712521065072,
          -57.533859760139535,
          -57.79181824091577,
          -58.052748467975825,
          -58.31220874205509,
          -58.5723088868142,
          -58.833604416417074,
          -59.09772737102568,
          -59.361570399724314,
          -59.625061289337665,
          -59.887723101503454,
          -60.14630337617529,
          -60.400522243944295,
          -60.65710277365724,
          -60.90423173572673,
          -61.1488480029457,
          -61.39992955238983,
          -61.642869706520315,
          -61.884112713830014,
          -62.12798305831393,
          -62.367499252827734,
          -62.5989911168697,
          -62.83226971129024,
          -63.068067969165035,
          -63.29352201894287,
          -63.51869377171798,
          -63.744574060217595,
          -63.9632054081868,
          -64.17946918008111,
          -64.39087128100185,
          -64.59307288142473,
          -64.79774072629073,
          -64.99614119848623,
          -65.19018627749644,
          -65.38663935244789,
          -65.5791784738423,
          -65.77004746504917,
          -65.96283931597681,
          -66.15308611727723,
          -66.33529531489182,
          -66.51771575184496,
          -66.69709734865911,
          -66.86730509002842,
          -67.03571981630326,
          -67.20266167852309,
          -67.36236189113457,
          -67.5171315661556,
          -67.67207276242547,
          -67.82266881094722,
          -67.96788663045962,
          -68.11370491917054,
          -68.25574671714102,
          -68.3920826262183,
          -68.52880159768614,
          -68.65945337777421,
          -68.78769555534664,
          -68.9138116590175,
          -69.03735264394497,
          -69.15802800532765,
          -69.27768878207934,
          -69.39457963372257,
          -69.51133214403787,
          -69.62687921144068,
          -69.7393260983239,
          -69.85024232875082,
          -69.9596104934127,
          -70.06789635784469,
          -70.17622383472096,
          -70.28477731920614,
          -70.39338978148825,
          -70.50211593579483,
          -70.61170336267585,
          -70.72176317533427,
          -70.8316308284024,
          -70.93848200194604,
          -71.04682356266727,
          -71.15713819051456,
          -71.26310597183229,
          -71.36791507471087,
          -71.47429848460003,
          -71.58049798198662,
          -71.68947274577285,
          -71.79898023393233,
          -71.9086231587463,
          -72.01462225740896,
          -72.12003512988949,
          -72.22491050130363,
          -72.32694776170058,
          -72.42697346969334,
          -72.5256454083299,
          -72.61945798242765,
          -72.7071885146368,
          -72.79224341616671,
          -72.8749685885782,
          -72.95711888288096,
          -73.03644209778228,
          -73.11470831988068,
          -73.19403338250781,
          -73.27356732183902,
          -73.35080617233405,
          -73.4277729671337,
          -73.501169825925,
          -73.57255014380672,
          -73.64150808359304,
          -73.70859952090991,
          -73.77128668775255,
          -73.82999345515604,
          -73.88400820460873,
          -73.93194521593419,
          -73.97965887212314,
          -74.01613727503462,
          -74.04693529831493,
          -74.0711026333788,
          -74.0891947739312,
          -74.10325171556272,
          -74.11077181359764,
          -74.11224291845295,
          -74.10828877711101,
          -74.0995104973766,
          -74.08196665257952,
          -74.05749153338483,
          -74.02688759415784,
          -73.98220592122641,
          -73.93424848937234,
          -73.88049603108865,
          -73.81435573295539,
          -73.74277211899157,
          -73.65782746601664,
          -73.56386568216291,
          -73.46030199570448,
          -73.34927496015943,
          -73.22821280892013,
          -73.09456365374437,
          -72.95534846178123,
          -72.79194288760058,
          -72.61153947551863,
          -72.42478106331122,
          -72.21697852077787,
          -72.00260673344646,
          -71.79210803903807,
          -71.56718201144498,
          -71.33436197572068,
          -71.09789845810721,
          -70.84104591911839,
          -70.57407981936726,
          -70.30955852147622,
          -70.03324249063157,
          -69.74250551351156,
          -69.45126632532073,
          -69.15049988756635,
          -68.83555389653114,
          -68.51632900035767,
          -68.18579209814202,
          -67.8591784862852,
          -67.52711456750755,
          -67.18935273017047,
          -66.8467766567328,
          -66.50913836766722,
          -66.17689903230985,
          -65.8340396162566,
          -65.49895269304913,
          -65.17246795909914,
          -64.84161569730651,
          -64.51065992391854,
          -64.1835038915548,
          -63.853982286047746,
          -63.518785170244925,
          -63.187701230962915,
          -62.852965890122164,
          -62.51342907730107,
          -62.16892689916969,
          -61.82381178700715,
          -61.47193908943564,
          -61.116189280358064,
          -60.76282956869246,
          -60.404002941780696,
          -60.04598434886867,
          -59.69282519615926,
          -59.3355286987274,
          -58.97310781191996,
          -58.61453102387709,
          -58.250098536509334,
          -57.87932129976984,
          -57.5116168124708,
          -57.14338302489704,
          -56.77321915078401,
          -56.406310194796994,
          -56.03706174316875,
          -55.66348173484058,
          -55.29385376614534,
          -54.918175066708905,
          -54.53869383123781,
          -54.165367036136196,
          -53.79573585058121,
          -53.416813290274135,
          -53.049804785035974,
          -52.6926426026352,
          -52.317505681165656,
          -51.95627625284769,
          -51.59828188664619,
          -51.22393505513749,
          -50.859494122315446,
          -50.50313720286346,
          -50.134912510661984,
          -49.76719458920423,
          -49.41273356824788,
          -49.05769279857246,
          -48.68567417822952,
          -48.320252811100765,
          -47.961158080307854,
          -47.589422946578104,
          -47.219485378610656,
          -46.86196010809194,
          -46.494724550229684,
          -46.122710718837624,
          -45.76135235637507,
          -45.393067032803195,
          -45.01750524526487,
          -44.65563382811126,
          -44.29875536440921,
          -43.94205462077312,
          -43.59641488842708,
          -43.24954644027592,
          -42.914529220701965,
          -42.574872968087384,
          -42.23274150579978,
          -41.889634041074956,
          -41.53797942480727,
          -41.1911990771342,
          -40.83934144669573,
          -40.47686020806958,
          -40.10907247027804,
          -39.74284072565406,
          -39.370736601841465,
          -38.99759851659228,
          -38.62990285959735,
          -38.25927149692369,
          -37.90318501940935,
          -37.55408283226934,
          -37.166623151450565,
          -36.8072200946209,
          -36.46453107940023,
          -36.128300651418876,
          -35.7763325115361,
          -35.428569609206676,
          -35.08406897859184,
          -34.74486171144833,
          -34.39238648350678,
          -34.043556708428305,
          -33.704591975519946,
          -33.369973164503264,
          -33.02009351016525,
          -32.67145044945371,
          -32.34029104081088,
          -31.994903242438408,
          -31.632808495022406,
          -31.28420150444608,
          -30.94808069482364,
          -30.603704159974015,
          -30.257207380248254,
          -29.935797232362642,
          -29.629354078135176,
          -29.304974384635095,
          -28.982420528642937,
          -28.674891263915935,
          -28.357181273736156,
          -28.034906293558503,
          -27.722810937030946,
          -27.404920432311187,
          -27.091178198832235,
          -26.784810356529796,
          -26.478407622341198,
          -26.172518449022466,
          -25.882606313413188,
          -25.596617669386553,
          -25.31453978147959,
          -25.05390906041133,
          -24.79162688852437,
          -24.52846305266152,
          -24.284195927541965,
          -24.052768889441175,
          -23.827648996882292,
          -23.613913911141825,
          -23.41927575372894,
          -23.236386968614017,
          -23.067603123255417,
          -22.923615727124492,
          -22.792925001168992,
          -22.670437417729644,
          -22.57089391261818,
          -22.484266716557016,
          -22.4067478490948,
          -22.344300745758325,
          -22.29419816744857,
          -22.25345585392556,
          -22.223168234744026,
          -22.20442084963895,
          -22.196149841969746,
          -22.19559734872195,
          -22.20184814816654,
          -22.21540543056247,
          -22.236235750390676,
          -22.263721066747788,
          -22.29830980446049,
          -22.339697232955015,
          -22.38933498422438,
          -22.446094186534943,
          -22.506256163603172,
          -22.570743553814037,
          -22.641006816368133,
          -22.71519314874621,
          -22.791179347569532,
          -22.87099126784645,
          -22.959337521455176,
          -23.045615996691463,
          -23.133909052688374,
          -23.228763257555926,
          -23.32352023053608,
          -23.41722304572924,
          -23.51645027077434,
          -23.61365317364001,
          -23.71032232278593,
          -23.813225598005634,
          -23.916403884699655,
          -24.0184935966503,
          -24.12572634325993,
          -24.23460642583712,
          -24.34153043183256,
          -24.449640124412333,
          -24.560573724624394,
          -24.66885722620413,
          -24.778775825390326,
          -24.890884635331997,
          -25.001748186045617,
          -25.11207307827067,
          -25.223034111710778,
          -25.33482529744038,
          -25.45046818840307,
          -25.56512873329032,
          -25.681520692822403,
          -25.798817957352274,
          -25.91524350757026,
          -26.03002243635211,
          -26.143763577234296,
          -26.261303446326345,
          -26.378715497757252,
          -26.49573694808921,
          -26.615050922919693,
          -26.73533115676734,
          -26.857122051466344,
          -26.980457917951913,
          -27.107964023508945,
          -27.23607163317926,
          -27.36648567972102,
          -27.501538580892056,
          -27.635394845876924,
          -27.7731271784617,
          -27.91813098687874,
          -28.063598752924364,
          -28.210489899091275,
          -28.3690240199239,
          -28.525881151008605,
          -28.67540648404655,
          -28.83542775015255,
          -28.995631100008875,
          -29.149310986007713,
          -29.312150932910924,
          -29.480085566937127,
          -29.63891981710694,
          -29.79867940438424,
          -29.966136471328255,
          -30.12500452839244,
          -30.285518039199967,
          -30.450265333170695,
          -30.61569229003806,
          -30.77587338589635,
          -30.93508740824461,
          -31.09540284954392,
          -31.258388061342448,
          -31.41888294932133,
          -31.57511818464571,
          -31.737554664825634,
          -31.896783844435237,
          -32.053913423833016,
          -32.2114636332057,
          -32.37285461287056,
          -32.531051429290095,
          -32.68885754441402,
          -32.849919198020686,
          -33.00869883027609,
          -33.169217120024626,
          -33.32953013097244,
          -33.49035867659496,
          -33.646755494579786,
          -33.802256803579,
          -33.955449110026514,
          -34.10296899335835,
          -34.250813973129034,
          -34.39329342626929,
          -34.52784724879321,
          -34.64676426306048,
          -34.752619918620674,
          -34.85377242376047,
          -34.950183775080376,
          -35.0431327394526,
          -35.13238961508849,
          -35.21874391813624,
          -35.30281467880575,
          -35.381490817891525,
          -35.4582819949889,
          -35.53996193367997,
          -35.616590107385285,
          -35.68956565653621,
          -35.76184809414489,
          -35.829051701971274,
          -35.893337102969625,
          -35.959892861350184,
          -36.022430691597776,
          -36.080563598518474,
          -36.141196549900215,
          -36.19420986742409,
          -36.238498716166326,
          -36.283105563442625,
          -36.32311202516677,
          -36.35841697035875,
          -36.393616704528924,
          -36.42838685123053,
          -36.461653021008956,
          -36.495958607085576,
          -36.52883412950095,
          -36.55988560497902,
          -36.589851425797285,
          -36.61854055322231,
          -36.64555510450045,
          -36.67180243832743,
          -36.698966839607515,
          -36.726416047033425,
          -36.75468946679683,
          -36.784307222512474,
          -36.81465248395067,
          -36.85061933889827,
          -36.88839578271501,
          -36.92881176290857,
          -36.970508841199,
          -37.0124036301459,
          -37.05516878506645,
          -37.10048210395789,
          -37.14931223859016,
          -37.201847743513774,
          -37.25415119973633,
          -37.304060846615926,
          -37.35504341018441,
          -37.40645438665597,
          -37.45525506765074,
          -37.50498196766519,
          -37.55530352161304,
          -37.60141837390055,
          -37.64822888551679,
          -37.694669500420986,
          -37.73974673067676,
          -37.788065496143844,
          -37.83668534628448,
          -37.8833431924286,
          -37.92992269066535,
          -37.97776682788842,
          -38.025260366043135,
          -38.07608450505955,
          -38.130903931610774,
          -38.18601668684481,
          -38.24546539137898,
          -38.30471364862205,
          -38.36127910163396,
          -38.42337867460787,
          -38.49053103356383,
          -38.559046235963514,
          -38.63070092178023,
          -38.70786239381107,
          -38.78697439848398,
          -38.87259986043353,
          -38.9602754610177,
          -39.04790578092653,
          -39.14281320903069,
          -39.24095898243617,
          -39.34093970189105,
          -39.44555304012069,
          -39.55552261316482,
          -39.67188470694354,
          -39.79273439752751,
          -39.921398871028515,
          -40.05825434488069,
          -40.203954986859465,
          -40.35927436739419,
          -40.52298427492694,
          -40.70148877232968,
          -40.89172554297195,
          -41.088991989474486,
          -41.301719994357086,
          -41.53137312305492,
          -41.76659644905784,
          -42.0033102063515,
          -42.266706122545244,
          -42.55190916660074,
          -42.83431239110593,
          -43.11980664808165,
          -43.41643315967788,
          -43.704789850167394,
          -43.99378305087913,
          -44.284294004099976,
          -44.56733231697766,
          -44.84901880223397,
          -45.14262932561309,
          -45.39503423546914,
          -45.64718664193296,
          -45.89280238506646,
          -46.126440530149985,
          -46.35065560107665,
          -46.56234101265238,
          -46.761896887716475,
          -46.95158941523801,
          -47.12938539508751,
          -47.29836031322895,
          -47.45544865766907,
          -47.60394811544859,
          -47.74295632423858,
          -47.87106068008201,
          -47.993593223548224,
          -48.10976556269096,
          -48.21892041048798,
          -48.32369685749149,
          -48.422170680874856,
          -48.51669582792246,
          -48.610401463933925,
          -48.70169559739552,
          -48.79147168802411,
          -48.882838260999215,
          -48.975189263300585,
          -49.06928345423546,
          -49.166417832837865,
          -49.266457713987485,
          -49.3714375898157,
          -49.480223195598334,
          -49.59149892689455,
          -49.70678305324979,
          -49.826808801777645,
          -49.95194004448032,
          -50.082452297263266,
          -50.21807923079181,
          -50.361558018743985,
          -50.514409024277334,
          -50.67061672461271,
          -50.834204484430636,
          -51.00830436447421,
          -51.184348015706426,
          -51.366044215941244,
          -51.550840106418335,
          -51.7459946678317,
          -51.942738181755246,
          -52.13879522193111,
          -52.34981877110988,
          -52.56250856672601,
          -52.76912675684228,
          -52.983814961013,
          -53.20988218085747,
          -53.431262921729946,
          -53.65561601212929,
          -53.890473672877825,
          -54.12368164840494,
          -54.35454687599877,
          -54.59398972802996,
          -54.83470042125781,
          -55.072299763695455,
          -55.31706067977363,
          -55.56017187087555,
          -55.80896819330829,
          -56.05888353134362,
          -56.305095144594596,
          -56.553294781269116,
          -56.803129973270366,
          -57.05278402075685,
          -57.302251695235306,
          -57.558426812495306,
          -57.81186606034034,
          -58.06452826636794,
          -58.320173441964805,
          -58.571170087697595,
          -58.81734892790467,
          -59.06261893753183,
          -59.30592263046282,
          -59.540753466804894,
          -59.77839893293952,
          -60.01597097146128,
          -60.246152471621585,
          -60.482093510196215,
          -60.71311524881444,
          -60.935457803639665,
          -61.159174954753766,
          -61.38275356524102,
          -61.604117530256154,
          -61.815999437562795,
          -62.02546661288117,
          -62.23627981905073,
          -62.437549724307544,
          -62.632319914357566,
          -62.81756671724356,
          -62.990131744697436,
          -63.15967130606996,
          -63.3191309661283,
          -63.46876535000585,
          -63.61110191209921,
          -63.746722989349834,
          -63.87263456611171,
          -63.992556969555906,
          -64.10112727749845,
          -64.19547178489243,
          -64.27681153071063,
          -64.34420266388581,
          -64.39943343354585,
          -64.44347929525618,
          -64.48128483890173,
          -64.50311173822463,
          -64.5120139442953,
          -64.5096371015061,
          -64.49850153409362,
          -64.47950075523246,
          -64.45163045449058,
          -64.41416220760645,
          -64.36897675213383,
          -64.31384599841805,
          -64.2493267477937,
          -64.17706346934067,
          -64.09761794367536,
          -64.00927862738813,
          -63.91159264663967,
          -63.80749746454112,
          -63.696547442040384,
          -63.57789532984996,
          -63.45432440947033,
          -63.32320996893662,
          -63.18565827365563,
          -63.04502521405786,
          -62.89976067033772,
          -62.752920552544374,
          -62.600480222341616,
          -62.44721397224273,
          -62.290612511229114,
          -62.12647951509279,
          -61.96072754865706,
          -61.79657756608333,
          -61.62487085156758,
          -61.45062504191556,
          -61.275425740967925,
          -61.09571027256372,
          -60.91222915922305,
          -60.72632851819106,
          -60.54625517509737,
          -60.36409377513301,
          -60.17779025002081,
          -59.9958028602795,
          -59.812472784514306,
          -59.62777059657209,
          -59.44413951121483,
          -59.260975869043435,
          -59.088850214626156,
          -58.914916575313356,
          -58.7475783916765,
          -58.59426034776173,
          -58.436836148636466,
          -58.29010923648031,
          -58.15007357386761,
          -58.01089684352622,
          -57.88490424849898,
          -57.77295261524937,
          -57.65768987481995,
          -57.553667457432866,
          -57.46312017780374,
          -57.372386975243636,
          -57.2919274731208,
          -57.22319484214453,
          -57.15656172906295,
          -57.09982847861494,
          -57.049924400068825,
          -57.00840937187823,
          -56.975832459024005,
          -56.94719294332324,
          -56.922234480091596,
          -56.901077370392734,
          -56.88110958657552,
          -56.86118869640121,
          -56.84088613130771,
          -56.821132914215454,
          -56.815002106926656,
          -56.80979611381951,
          -56.80517883350121,
          -56.80051808684475,
          -56.79644297281487,
          -56.79289144647149,
          -56.78943010656069,
          -56.786233593180526,
          -56.78345673966681,
          -56.7811665630323,
          -56.75996454540282,
          -56.7363381058681,
          -56.71233840244565,
          -56.68787842570376,
          -56.662983636726814,
          -56.63763657016417,
          -56.61183675452828,
          -56.58564663370481,
          -56.558692202886405,
          -56.531097615057625,
          -56.52434464810236,
          -56.5199519386102,
          -56.515403388683794,
          -56.51087858954138,
          -56.5063573209964,
          -56.5017161581568,
          -56.497114993181945,
          -56.49246965306654,
          -56.48776828222017,
          -56.48304234668775,
          -56.46702078317542,
          -56.44969022770539,
          -56.43226281970084,
          -56.41484371752729,
          -56.39738923996846,
          -56.379895753924686,
          -56.362391804866704,
          -56.34484174931023,
          -56.327259820587955,
          -56.309596904818946,
          -56.3033488562526,
          -56.298236827300386,
          -56.293065661739035,
          -56.287957444135024,
          -56.28290294654708,
          -56.27772258408275,
          -56.27251843788752,
          -56.2673617287949,
          -56.26207736656889,
          -56.2568281989473,
          -56.2275274174694,
          -56.19506507780273,
          -56.162582375227316,
          -56.13019612303026,
          -56.09797893912742,
          -56.06577374827643,
          -56.03345300393017,
          -56.00125422789405,
          -55.96918269502179,
          -55.93673707253973,
          -55.92987352379566,
          -55.9259372303979,
          -55.92209594057085,
          -55.918427741871454,
          -55.91475993280608,
          -55.91110545407247,
          -55.90740545539027,
          -55.90330183965871,
          -55.89952828966962,
          -55.89582850535093,
          -55.894829120635116,
          -55.893883172380534,
          -55.89308540843156,
          -55.892279575204036,
          -55.891315691557,
          -55.89038851536575,
          -55.88954197162121,
          -55.88865548285507,
          -55.887708389988845
         ],
         "y": [
          45.299718434481434,
          45.30013974702479,
          45.30063571154232,
          45.30114686375785,
          45.30150261131389,
          45.3017899970426,
          45.30236707808463,
          45.30287884751629,
          45.3035273124906,
          45.30408450232165,
          45.30460802412102,
          45.30524000954758,
          45.305893681440025,
          45.30642718230222,
          45.306953849677924,
          45.30758655349011,
          45.30817058079298,
          45.308765977677744,
          45.30916949728607,
          45.309576423754294,
          45.30999953180667,
          45.310472382304106,
          45.310869975986996,
          45.31131992004422,
          45.3117136569928,
          45.31213422949182,
          45.31252989359154,
          45.31286838849167,
          45.31318042227869,
          45.313520830069514,
          45.31378112954761,
          45.314042891621064,
          45.3143255803598,
          45.31459079192223,
          45.314915446046335,
          45.315213503667415,
          45.31547083747926,
          45.31568919264709,
          45.315949555167926,
          45.316230264771434,
          45.31642204305476,
          45.31667953636436,
          45.31701735727197,
          45.31719809178335,
          45.31736415483957,
          45.317553916882986,
          45.31779573502166,
          45.31797146615517,
          45.31815950894265,
          45.31838925028085,
          45.31859991944094,
          45.318852018727746,
          45.319099285855756,
          45.31929173583678,
          45.319490588135054,
          45.31968722633857,
          45.3199187057454,
          45.3201108558734,
          45.32024283799233,
          45.320447928901416,
          45.32058641481309,
          45.3207734550583,
          45.320974930400254,
          45.32112493246592,
          45.321286050816404,
          45.32147070970754,
          45.32164142123714,
          45.32202703316613,
          45.32254705800193,
          45.32301875091753,
          45.32346885341235,
          45.32401104849823,
          45.324593452118236,
          45.32510954271194,
          45.32559590644499,
          45.326135359662985,
          45.32673746967972,
          45.327148770307815,
          45.32757959164762,
          45.32804989611945,
          45.32840617801765,
          45.328830825116064,
          45.32934855748933,
          45.32975924646779,
          45.33014891795632,
          45.330666778999976,
          45.33114515148283,
          45.33166922226085,
          45.33227448848537,
          45.33285895295016,
          45.333431930156806,
          45.33396327881899,
          45.334506865189574,
          45.33508755040129,
          45.33562600519236,
          45.33616278148277,
          45.33666823981242,
          45.33715002225605,
          45.33749402104377,
          45.3378002849158,
          45.338204896435045,
          45.33858942999313,
          45.33885646317251,
          45.33915047530712,
          45.339397152283055,
          45.33977023237858,
          45.34019352087018,
          45.34050336250638,
          45.34087238457947,
          45.34123706047124,
          45.34159301383292,
          45.3420204810963,
          45.34241525119844,
          45.342737730564025,
          45.343089890197156,
          45.34346947381766,
          45.343877097795875,
          45.344283396952605,
          45.34457099063465,
          45.34485192241254,
          45.34521201475351,
          45.34558913175783,
          45.34590903170268,
          45.34618959737896,
          45.34653486909946,
          45.34691220323054,
          45.347271394714035,
          45.34754169409517,
          45.34773696126847,
          45.34806415342266,
          45.34841192672122,
          45.34863862528806,
          45.348917300136186,
          45.34929052345286,
          45.34952539985571,
          45.349908144116874,
          45.350149840272444,
          45.35036920642808,
          45.35049867688795,
          45.35079137871575,
          45.35110058592429,
          45.35124302567623,
          45.35147245537082,
          45.35174403836285,
          45.35202228803002,
          45.35235141245206,
          45.35263531962548,
          45.352850133960885,
          45.35315828262761,
          45.35360275870033,
          45.35381100387733,
          45.354015574240876,
          45.35429750230924,
          45.354598633230985,
          45.35485305326219,
          45.35503844423474,
          45.35518332085755,
          45.355298077054144,
          45.355554716864894,
          45.35577485070798,
          45.35591374938485,
          45.35606529705287,
          45.35631288796946,
          45.35662317568206,
          45.35704873448834,
          45.35724478362889,
          45.3574322394342,
          45.35776813085408,
          45.35827647169903,
          45.358993093937855,
          45.359484524864584,
          45.35988466028037,
          45.360457989654854,
          45.36105480217147,
          45.36159448796326,
          45.36212316190755,
          45.36265534864159,
          45.36315123310733,
          45.36364058951429,
          45.36415365574575,
          45.36462535441737,
          45.36508600318736,
          45.365574105334055,
          45.36607946422612,
          45.36654579849777,
          45.36704170154077,
          45.367534887791635,
          45.36792576494745,
          45.36824359412654,
          45.36860242175758,
          45.36901586722353,
          45.369431327282356,
          45.36981859469267,
          45.37010287348836,
          45.370431506244174,
          45.37081576962552,
          45.37116814001007,
          45.37147989284605,
          45.371708942071166,
          45.371994700159625,
          45.37237211183017,
          45.37260933731308,
          45.37287272161522,
          45.373185633182736,
          45.37358584990655,
          45.374231086817765,
          45.37463113642426,
          45.3752267849971,
          45.37577063238242,
          45.37629185712969,
          45.37785964432921,
          45.380910216409134,
          45.38617583063742,
          45.39429231259471,
          45.40556256610919,
          45.419621192537164,
          45.434869706598384,
          45.449319283626465,
          45.461055341864586,
          45.4702245686378,
          45.476840328805594,
          45.481741220634696,
          45.4851970429676,
          45.487556127879074,
          45.48961027497986,
          45.49209305494798,
          45.495681503693234,
          45.5015125032667,
          45.50976071472965,
          45.52044139833738,
          45.533528007324854,
          45.548705950369374,
          45.56547029537028,
          45.58344988667698,
          45.60219700821508,
          45.62155458682291,
          45.64131175768604,
          45.66107190257342,
          45.68058405608774,
          45.699084214421234,
          45.71513592310621,
          45.72692820998699,
          45.73296659798701,
          45.73228577610344,
          45.72478547695079,
          45.709062265710436,
          45.68362931552094,
          45.648436638923904,
          45.6005590076713,
          45.54143022575991,
          45.47090161889065,
          45.38532656442469,
          45.287275538844284,
          45.17602499405964,
          45.05258492662113,
          44.915518150037336,
          44.76668684699259,
          44.61138974751405,
          44.44210175245866,
          44.26121033544627,
          44.07218039214349,
          43.871952149589525,
          43.6559605939235,
          43.43215626095299,
          43.20088398599591,
          42.95980262188665,
          42.7066848852861,
          42.44721022482909,
          42.19139453924118,
          41.92009323109292,
          41.637968510937874,
          41.38158954687498,
          41.10566257344352,
          40.81940390385516,
          40.536771920455365,
          40.250119352401605,
          39.96497931607584,
          39.671763886065285,
          39.36561448117603,
          39.07776853498432,
          38.78177220721696,
          38.469709243214545,
          38.1741102843626,
          37.87541437027626,
          37.562343323161734,
          37.25458553859626,
          36.95009843762025,
          36.6420838233015,
          36.32836054955793,
          36.017065111071396,
          35.706307861354105,
          35.39298610169376,
          35.08713300691843,
          34.78053963067478,
          34.46585239272821,
          34.16073274696967,
          33.85785656816834,
          33.54907006348222,
          33.227535361675486,
          32.92284224858699,
          32.612054841562994,
          32.28347767411683,
          31.962557944624518,
          31.64741134177734,
          31.323628803847757,
          30.991931591852087,
          30.678251753168134,
          30.357053326498573,
          30.021636992706057,
          29.69641475409675,
          29.38114451722201,
          29.0529807876609,
          28.728670196043417,
          28.414933994334607,
          28.090089622494144,
          27.768404888564156,
          27.44341361720266,
          27.124451282605364,
          26.80030761476627,
          26.472147653847113,
          26.15321433224592,
          25.83227239584316,
          25.515193337579735,
          25.18402986331489,
          24.872502961866697,
          24.55917164764911,
          24.229671287982033,
          23.907246162616186,
          23.586484310217152,
          23.26357655551848,
          22.931446184257094,
          22.599980187960238,
          22.27444689632395,
          21.94300759057357,
          21.611178204578085,
          21.280281711262774,
          20.949274543673777,
          20.612428582052907,
          20.279241690577816,
          19.944961979066782,
          19.595267171610544,
          19.259262663045853,
          18.924220664589885,
          18.57185009209973,
          18.220623855561502,
          17.87645459159285,
          17.514145952525595,
          17.15378437989861,
          16.795532783890447,
          16.42789815116257,
          16.06968735391795,
          15.706132269368716,
          15.334544702668433,
          14.970436603584684,
          14.603678506298932,
          14.221207066737518,
          13.849615250578609,
          13.475084425184,
          13.084228921148902,
          12.706312703669063,
          12.32769580443048,
          11.938432352067267,
          11.556455460116831,
          11.17793251207936,
          10.784890990753082,
          10.391839837392332,
          10.010067844493385,
          9.620242422889108,
          9.23219747383752,
          8.850523047061543,
          8.470468283710078,
          8.08419987199292,
          7.697968232820205,
          7.311387319346879,
          6.92510609587932,
          6.533090560048482,
          6.145142317640205,
          5.757666940316765,
          5.363570563632581,
          4.9756568144842745,
          4.585886155497769,
          4.1905936097729555,
          3.801351940174415,
          3.41798755083955,
          3.028529933190099,
          2.6441059141994376,
          2.27294101898256,
          1.856458096383074,
          1.4757070871246285,
          1.1073339766813302,
          0.7402110061908301,
          0.37133908131931304,
          0.009268102579207183,
          -0.3457574475286201,
          -0.7019142405637846,
          -1.0528789878397145,
          -1.3998820125069955,
          -1.748833447218612,
          -2.0891258901127263,
          -2.4350264130741515,
          -2.785304479979115,
          -3.127946758194442,
          -3.473779161421556,
          -3.8291551568676474,
          -4.175866904769248,
          -4.512490675048943,
          -4.865137311174306,
          -5.203824063105863,
          -5.525428504572238,
          -5.864225366552495,
          -6.1934773822465194,
          -6.50552746940229,
          -6.827145053616824,
          -7.140766272701244,
          -7.4390147475393675,
          -7.738128503613352,
          -8.016994525444474,
          -8.286986912703423,
          -8.554893537359042,
          -8.799055506627557,
          -9.036050212755432,
          -9.269804210267157,
          -9.481770440048242,
          -9.68514090025804,
          -9.8825226452152,
          -10.05848048544291,
          -10.223649914517283,
          -10.376832739330755,
          -10.51179117091306,
          -10.625221040234637,
          -10.718551990605059,
          -10.78307430643003,
          -10.824965206016069,
          -10.849411350416643,
          -10.85139176078873,
          -10.82953169832549,
          -10.779750369459013,
          -10.705911849149164,
          -10.61298179251615,
          -10.49391067136101,
          -10.350766286003042,
          -10.186750919467716,
          -9.999394790259581,
          -9.79340996295848,
          -9.571596565786326,
          -9.328850536567419,
          -9.07259253143243,
          -8.802643265996876,
          -8.517846586137384,
          -8.221934394019296,
          -7.916477216537806,
          -7.596357269582938,
          -7.271702008812883,
          -6.936659116357311,
          -6.589647711483182,
          -6.239218289766555,
          -5.8808913029715,
          -5.513012902334701,
          -5.143407059275042,
          -4.7702321530630165,
          -4.39279341333818,
          -4.011544482728926,
          -3.632042918431274,
          -3.2515495911424566,
          -2.8706436719586867,
          -2.4889554275436208,
          -2.1076317650996987,
          -1.722980415101513,
          -1.3319706820070059,
          -0.9476356750613282,
          -0.5692006826162967,
          -0.18486554621349793,
          0.19177756857133768,
          0.5591343653191786,
          0.9330755093307356,
          1.3130695247353235,
          1.668335501336059,
          2.026710924675365,
          2.395607639437436,
          2.7395694832199577,
          3.091391319017581,
          3.4504230238737565,
          3.785974770069895,
          4.127158137604507,
          4.473588339007547,
          4.798607039033906,
          5.128483228468712,
          5.461247205304259,
          5.7655720498109835,
          6.067001276667719,
          6.386035219520769,
          6.690737910994235,
          6.983572461445581,
          7.294810123032193,
          7.600664154524186,
          7.887940111141231,
          8.189534055963769,
          8.494710828262713,
          8.787944134083013,
          9.089908475778346,
          9.396032782226843,
          9.695039455568445,
          10.001482738587534,
          10.309826726403713,
          10.616670528201501,
          10.927144917211407,
          11.237467369938699,
          11.546610029571692,
          11.862483991377665,
          12.178504454089424,
          12.499498488895368,
          12.826413684488807,
          13.16268807738713,
          13.501623699204668,
          13.844831221993385,
          14.192886668940524,
          14.543329633718544,
          14.893128370914617,
          15.24878032105807,
          15.609834546852696,
          15.979671300259401,
          16.35936206302697,
          16.748549500796656,
          17.142047565456913,
          17.540025105362574,
          17.941856171873095,
          18.345344946496976,
          18.75984374133597,
          19.181929054644538,
          19.605205658104733,
          20.02302033658512,
          20.442662642128155,
          20.86771243508503,
          21.292999017297102,
          21.722163313318603,
          22.151078902835863,
          22.587714870984676,
          23.029974944912194,
          23.45741883619464,
          23.887343065941536,
          24.331733065699446,
          24.767102537829327,
          25.204996765771696,
          25.651895296889773,
          26.10077990944607,
          26.54195298933848,
          26.982260825027105,
          27.425128176576813,
          27.862844339234286,
          28.299885433274653,
          28.753022624041996,
          29.20088045582045,
          29.63810338480583,
          30.091352763500165,
          30.54192730345249,
          30.97446726905821,
          31.428574818885732,
          31.87858895660617,
          32.31684114625722,
          32.77663596869445,
          33.23856387174748,
          33.68254988557835,
          34.14938978863933,
          34.613864356845774,
          35.061688999591375,
          35.53232232805609,
          35.99736162284397,
          36.442166119780346,
          36.90088174463004,
          37.34261803819572,
          37.78440266390773,
          38.23778605939985,
          38.682875278383925,
          39.1220452773332,
          39.560964175837675,
          39.9879118137015,
          40.41426254539005,
          40.85459174029404,
          41.27966374565932,
          41.714394888999884,
          42.15154032030003,
          42.56496434196218,
          42.98446922691957,
          43.407134447006655,
          43.799038515324206,
          44.208977672828986,
          44.62151561116713,
          45.00893355671741,
          45.399683171035534,
          45.78761048775274,
          46.16170088818614,
          46.517655009136895,
          46.87465502207902,
          47.22198568565066,
          47.556843273577904,
          47.88657827671448,
          48.197671938606085,
          48.504250466129676,
          48.80945175274481,
          49.10156254666932,
          49.387723910464985,
          49.663963228244945,
          49.93547473105268,
          50.20682153355503,
          50.46915343670965,
          50.73415436196795,
          51.00762638157096,
          51.265193279432815,
          51.52898761067486,
          51.80565998422979,
          52.06979113005717,
          52.3374184984377,
          52.62198242960895,
          52.88887632021847,
          53.13652760244822,
          53.400097811866836,
          53.66251131653647,
          53.90445457836404,
          54.148481490728166,
          54.39349952947101,
          54.623062075947814,
          54.845516176624216,
          55.06405268457755,
          55.27260353632475,
          55.474568221008,
          55.67091792567738,
          55.86447039743989,
          56.05864867993102,
          56.24866552618537,
          56.43021379205581,
          56.610413816557354,
          56.78715684713698,
          56.955495457294504,
          57.11927878250059,
          57.28203357398337,
          57.43671511441069,
          57.574630312304805,
          57.705510415894544,
          57.835600156804055,
          57.948661288221594,
          58.056433788488995,
          58.166337838612584,
          58.26478493445352,
          58.35488297879964,
          58.44709736338487,
          58.536642329987835,
          58.62357865105658,
          58.715468251870966,
          58.8065326495339,
          58.8956919640694,
          58.98632877450392,
          59.07763340690364,
          59.16911483062227,
          59.2610262875103,
          59.353715803910546,
          59.44656242845687,
          59.54056291020131,
          59.633396953774316,
          59.727674662425315,
          59.82263572496919,
          59.92002879337948,
          60.01673053702014,
          60.1149554497501,
          60.21437594137841,
          60.31188757167649,
          60.40667423941273,
          60.503569609384655,
          60.59391001250553,
          60.68069824189817,
          60.76856181061859,
          60.85035285607706,
          60.92865332396755,
          61.00901663235724,
          61.08530036970657,
          61.1579708568082,
          61.23947846913224,
          61.314573324793386,
          61.38789174904695,
          61.461227712517555,
          61.53642352392255,
          61.60882835505364,
          61.678254184127354,
          61.74775833431579,
          61.81540779649075,
          61.88182080219317,
          61.94877899678814,
          62.01451179528355,
          62.07539832696194,
          62.13664749663531,
          62.19835750943565,
          62.25684351688425,
          62.31367673992014,
          62.369448462907485,
          62.42124931964589,
          62.47118969451585,
          62.51911025909183,
          62.5643019681068,
          62.60789583103667,
          62.64846958027227,
          62.687924221901426,
          62.725836468702795,
          62.762387471385054,
          62.79841944632367,
          62.83351905150026,
          62.868695798379285,
          62.902924958497266,
          62.93644674954601,
          62.97033210948266,
          63.00306015736388,
          63.03619020297542,
          63.06864193774922,
          63.100670138939414,
          63.13264698016124,
          63.16349918765155,
          63.193273338716864,
          63.22394150467434,
          63.256073790139574,
          63.289994807170864,
          63.32362329309499,
          63.35901355230254,
          63.39411268457746,
          63.428387436834186,
          63.46241222028587,
          63.4967296617323,
          63.52682094882466,
          63.5547675894417,
          63.57924482731159,
          63.59364229800525,
          63.597104207933505,
          63.589973932013265,
          63.573005082347024,
          63.54629652988308,
          63.510034210478096,
          63.462809643827065,
          63.40683170762029,
          63.3342011625207,
          63.24758795434877,
          63.15255794382895,
          63.04257681538751,
          62.92362129571702,
          62.79555055824176,
          62.652914340423955,
          62.49554621804873,
          62.32887212151441,
          62.146187451440724,
          61.95595683547793,
          61.7632949171735,
          61.55181887631534,
          61.32843895611934,
          61.101943844958896,
          60.862216410026456,
          60.61150680878929,
          60.35640260905442,
          60.09807585763194,
          59.82600904989316,
          59.55434354351422,
          59.28470199198781,
          59.00059902902347,
          58.707861829629316,
          58.42276912132257,
          58.12529707466105,
          57.81671397272391,
          57.51082495910958,
          57.18869645214282,
          56.86423947156095,
          56.535151086582914,
          56.192845116687735,
          55.84928555032313,
          55.50075464328807,
          55.149409976312725,
          54.79769945184625,
          54.44698362153218,
          54.096706162612975,
          53.743709295913376,
          53.39614795661498,
          53.04993354424443,
          52.70558761596855,
          52.36842284572481,
          52.03414162007931,
          51.702623876531554,
          51.370835228899004,
          51.03407171436232,
          50.69746261807563,
          50.373322353732895,
          50.04299787072454,
          49.705770127821246,
          49.38735525533109,
          49.060510811853995,
          48.72654359469327,
          48.39837977209214,
          48.08072854856022,
          47.75452253146979,
          47.42944116755567,
          47.1155725241505,
          46.79244682804856,
          46.467626569995666,
          46.151702190248166,
          45.8292167429687,
          45.502990015424785,
          45.17938716036984,
          44.85720971375609,
          44.525492671489545,
          44.192492880390596,
          43.86487148618212,
          43.527394975486594,
          43.190341149071514,
          42.85898798333011,
          42.52778486699666,
          42.19862233449117,
          41.87133250581469,
          41.53675172662458,
          41.21201284379724,
          40.884079589178135,
          40.547753097573086,
          40.21730789093999,
          39.88486738699658,
          39.55194229664582,
          39.22205392495302,
          38.89214369967228,
          38.559399991732164,
          38.2296817338311,
          37.90250431708949,
          37.568319985971456,
          37.241578581982324,
          36.917479880631426,
          36.58797100728486,
          36.26245884112828,
          35.94543369055382,
          35.62657591952224,
          35.31727339509226,
          35.00585671904028,
          34.68671640288381,
          34.38207220279461,
          34.07675083097773,
          33.762715685796266,
          33.444015436249614,
          33.14219928493705,
          32.82654199851878,
          32.49818148759017,
          32.17965533632465,
          31.86184362378993,
          31.541619123950866,
          31.214264888095485,
          30.902050300599047,
          30.588530913072027,
          30.264963162783282,
          29.949730656161847,
          29.635073113076377,
          29.319626887633856,
          29.003824174077053,
          28.693928414828797,
          28.384420771836822,
          28.070868989852066,
          27.76129562865431,
          27.447121910555577,
          27.13920364454229,
          26.829861640631954,
          26.51451931543211,
          26.213818487789933,
          25.910309771230075,
          25.602923559619786,
          25.295772151217005,
          25.00131852769632,
          24.705508344289374,
          24.400694098862083,
          24.069037142059887,
          23.770650168471438,
          23.463429690467894,
          23.146745727324166,
          22.8309992416603,
          22.518337589381826,
          22.20067248985571,
          21.882702293861733,
          21.56824074072042,
          21.24663983868902,
          20.92269709573191,
          20.60022027443589,
          20.28195184331143,
          19.955211297103826,
          19.626730938105542,
          19.31171750581098,
          18.98858179091357,
          18.656965688388144,
          18.334384526936276,
          18.008454892066144,
          17.66708395473627,
          17.337427911309227,
          17.013719013550592,
          16.670790836970745,
          16.337592369280337,
          16.015397605573686,
          15.67462497366007,
          15.339540589266472,
          15.018530345703198,
          14.676651760850092,
          14.331775623839576,
          14.009754581590677,
          13.637650212408312,
          13.281136798153804,
          12.951800864609703,
          12.615131051089216,
          12.258860228240723,
          11.9187579393447,
          11.57789390158883,
          11.223050074155491,
          10.873341690901782,
          10.523687391868252,
          10.166554889456599,
          9.811022414357117,
          9.456020377858247,
          9.100903652998541,
          8.750158985983907,
          8.395229134951304,
          8.037985110034583,
          7.682742899483137,
          7.324366851919589,
          6.964263587073127,
          6.603888882368382,
          6.252824518194672,
          5.891020870699171,
          5.531405672386699,
          5.177081777470986,
          4.813802372561208,
          4.451963739189691,
          4.090995219729578,
          3.727774677820828,
          3.36168838532809,
          3.0008321018421924,
          2.641543516871443,
          2.279111765583993,
          1.9168337173546421,
          1.5582123203951013,
          1.1996223339978025,
          0.8385918355327884,
          0.4808254145686994,
          0.12979181543773116,
          -0.22413403291554124,
          -0.5691012455811524,
          -0.9066823542473489,
          -1.241229619184098,
          -1.5732899174351296,
          -1.8995770661416154,
          -2.219694902437592,
          -2.5451530279516223,
          -2.8676134221602236,
          -3.1942237481503195,
          -3.5170686339268715,
          -3.8363874605060797,
          -4.197714871251118,
          -4.526329228339178,
          -4.841803876738634,
          -5.158672505485492,
          -5.482287674054555,
          -5.804824767867621,
          -6.115071052011439,
          -6.427658671448018,
          -6.741351839801882,
          -7.040627960359345,
          -7.342648513446687,
          -7.640580726166761,
          -7.909928498674154,
          -8.180489757848637,
          -8.453984438454636,
          -8.705336956341986,
          -8.947818543021045,
          -9.189655263630117,
          -9.41685446197051,
          -9.636423663430703,
          -9.848628239347748,
          -10.050138741681844,
          -10.243170565631027,
          -10.431450973305097,
          -10.609436771122674,
          -10.7821667520709,
          -10.945187722832038,
          -11.097407254984088,
          -11.238559238641908,
          -11.3666326213761,
          -11.478365323903308,
          -11.564914080634889,
          -11.629557490103016,
          -11.674596107296022,
          -11.696876356448303,
          -11.697352245294429,
          -11.676752317474575,
          -11.63449483230157,
          -11.571438008900385,
          -11.483399684290735,
          -11.37233264607733,
          -11.242877523136368,
          -11.088205242283749,
          -10.91056875650235,
          -10.718160389732232,
          -10.505390403873873,
          -10.273047338603224,
          -10.035556106735442,
          -9.777673079790448,
          -9.502533688776865,
          -9.2272971204055,
          -8.936788449605405,
          -8.63271952734524,
          -8.330509922735615,
          -8.017566487984993,
          -7.6950731376609625,
          -7.370192516103867,
          -7.040907752697563,
          -6.705000514000552,
          -6.365876617460091,
          -6.026181323894576,
          -5.6814681384112315,
          -5.3345401137271455,
          -4.987284086519732,
          -4.639743838543606,
          -4.294469330527796,
          -3.947484022729094,
          -3.605390912128818,
          -3.2651466286676394,
          -2.9240691824482448,
          -2.586496380041736,
          -2.250161547337725,
          -1.9136633110936039,
          -1.581305949194603,
          -1.2489914413368912,
          -0.9222156255151451,
          -0.6035045789681034,
          -0.2765286946560145,
          0.04137218537884545,
          0.35477961485070936,
          0.6634608219180338,
          0.9839620741974724,
          1.2989556210052042,
          1.5940082184992426,
          1.9042955664513466,
          2.213861720834922,
          2.506437533023011,
          2.805491823780999,
          3.1142433768799918,
          3.4059430044454757,
          3.695619840593113,
          3.995339418006365,
          4.281903490289008,
          4.564851886172743,
          4.855746893704478,
          5.138465675552538,
          5.413489986877798,
          5.689286808248597,
          5.967330587568085,
          6.238536138005329,
          6.507042690114719,
          6.775407574006047,
          7.045585969704588,
          7.309449764010907,
          7.5723985085288215,
          7.842220575059579,
          8.109555396134546,
          8.374119988514705,
          8.64442282897711,
          8.921310848286897,
          9.192569313460302,
          9.465006450503253,
          9.74493409671807,
          10.015831188524905,
          10.288190471128273,
          10.564148014719482,
          10.836869669755542,
          11.112199181272134,
          11.388103570023366,
          11.660245268410408,
          11.937327420051052,
          12.22035238673423,
          12.500843520726555,
          12.78598478054187,
          13.07675490219391,
          13.367905308542989,
          13.66281125320392,
          13.964202485517921,
          14.265349677648844,
          14.564895065825162,
          14.873363527118272,
          15.17767439391314,
          15.488244814187693,
          15.81096980609484,
          16.13688661774782,
          16.466180743034002,
          16.81161151063625,
          17.158775097569574,
          17.50404835518807,
          17.85839062136845,
          18.22047169463572,
          18.572945852675076,
          18.931854457309303,
          19.298604546159268,
          19.657525031722894,
          20.013298239763355,
          20.37683390267937,
          20.741021277886734,
          21.097254409597824,
          21.4650874339504,
          21.83556483746958,
          22.200648195698733,
          22.574209425164877,
          22.95101750668138,
          23.31549922460493,
          23.686787346742054,
          24.065527328103176,
          24.442428388728448,
          24.817619440541705,
          25.201725529021076,
          25.587511252661145,
          25.971495371479403,
          26.351701392202713,
          26.734579025955508,
          27.11994913277827,
          27.503247114367703,
          27.884579569813056,
          28.274581807396096,
          28.670825075468827,
          29.05828344423737,
          29.444369655159377,
          29.840481155694537,
          30.233112698734114,
          30.612579488717785,
          31.005186875526537,
          31.40026183882251,
          31.784034993281782,
          32.1767600092729,
          32.57839635990616,
          32.973788085172124,
          33.36707385723474,
          33.7747350773587,
          34.174867195432704,
          34.56565927007528,
          34.97269897372242,
          35.38099174232684,
          35.773274418694164,
          36.17188052679075,
          36.576210912661864,
          36.96590210487735,
          37.36045124150102,
          37.763519221555654,
          38.15592466177955,
          38.54705143584231,
          38.93957607209103,
          39.3252501621869,
          39.700663506512065,
          40.0767022581467,
          40.45821761035811,
          40.83428228061062,
          41.21088079845879,
          41.59903782760523,
          41.975886954303824,
          42.34046905396035,
          42.715320312597285,
          43.091465560146496,
          43.44936522764123,
          43.8092069440132,
          44.17622953167472,
          44.526079067298404,
          44.86735441023502,
          45.21638709862258,
          45.5461049856716,
          45.87635458468328,
          46.2000237449179,
          46.502226615595546,
          46.80576047816677,
          47.095318697331194,
          47.37578712277759,
          47.67164256501043,
          47.94343864522116,
          48.20589043275671,
          48.48325940919611,
          48.756924946637035,
          49.028377199005995,
          49.30363230442888,
          49.570889558757266,
          49.84634301215178,
          50.12768744689074,
          50.40895489953932,
          50.68343352813979,
          50.973440414634375,
          51.25861087042464,
          51.53085556400556,
          51.81766805132871,
          52.1050147640509,
          52.374967442266225,
          52.66039473441991,
          52.93390555095745,
          53.163167180092074,
          53.39940834873647,
          53.63822416578305,
          53.86074179851649,
          54.07701365947243,
          54.29386895756701,
          54.49971335955047,
          54.69685665335548,
          54.88883473806454,
          55.07533841403359,
          55.2639708544337,
          55.44340921058112,
          55.6153452312377,
          55.78231773439923,
          55.944807794529694,
          56.10256210045506,
          56.251104206942145,
          56.40120995073123,
          56.55155818927396,
          56.699635714050984,
          56.84899230943216,
          56.996418069619715,
          57.14424297262831,
          57.284734479281234,
          57.4194130306999,
          57.548906820982815,
          57.67551577901924,
          57.797573164866,
          57.92076478080977,
          58.041334590806294,
          58.154182211743525,
          58.26686528487959,
          58.38001533876473,
          58.491997052698785,
          58.602908337428495,
          58.71531936015631,
          58.827309263636785,
          58.93697907124501,
          59.04640275622206,
          59.1535203554293,
          59.26366343136951,
          59.373620509730934,
          59.48072217849345,
          59.58638357077552,
          59.690346099203815,
          59.79134802306432,
          59.890581611258135,
          59.98941652947211,
          60.087114248711984,
          60.18527892985866,
          60.281659385175374,
          60.376610175961304,
          60.47176002002214,
          60.56558070662002,
          60.65612145810298,
          60.749356352593466,
          60.841439717548006,
          60.93324770443983,
          61.027408169805604,
          61.117695948170216,
          61.2045982862352,
          61.29410255104259,
          61.381195932078256,
          61.46481315224713,
          61.550881215562875,
          61.63579468844195,
          61.714126687994906,
          61.795932589882604,
          61.87795318689741,
          61.954480203287204,
          62.03250571918005,
          62.109842296365365,
          62.181616376468,
          62.25242505552403,
          62.322987891037634,
          62.3880198885742,
          62.45218275526259,
          62.51655948768926,
          62.57709176450033,
          62.635301424366226,
          62.69445847580147,
          62.751419852966315,
          62.80751083418683,
          62.86266293527033,
          62.91770705234575,
          62.97150070976861,
          63.02489322387806,
          63.07811426752116,
          63.1314365399524,
          63.18582217685417,
          63.240760811207124,
          63.29610738279832,
          63.349196002358134,
          63.402238665549575,
          63.45430719454715,
          63.50527843059613,
          63.557342666072415,
          63.60613622365498,
          63.64945623342096,
          63.69104080081217,
          63.72936882520374,
          63.761744699570755,
          63.79052776083536,
          63.81878188577173,
          63.84581992116187,
          63.86872330072505,
          63.88951849870405,
          63.9102267618383,
          63.930799640352205,
          63.9479467658193,
          63.96411161136835,
          63.9809442578884,
          63.996950116555325,
          64.00983083328845,
          64.02031513663198,
          64.02394371680037,
          64.01834009142722,
          64.00298935037688,
          63.978349825407875,
          63.94582408675004,
          63.905179930672396,
          63.85325136599898,
          63.79161879404028,
          63.716599209905894,
          63.62170596504502,
          63.514439546560816,
          63.394067655483155,
          63.25752856365438,
          63.11203323564524,
          62.952839397423055,
          62.77460926932836,
          62.584505746832164,
          62.37551002067494,
          62.15314717829945,
          61.92615249192401,
          61.6810368107225,
          61.4212869485904,
          61.1545317132926,
          60.874904437163096,
          60.58021150000361,
          60.28828276463054,
          59.98743453016053,
          59.669637717004456,
          59.364048008832896,
          59.05164330443183,
          58.71497916071203,
          58.39252988437138,
          58.059631911515474,
          57.7107673804263,
          57.37080032709071,
          57.026701339767335,
          56.66154841804023,
          56.2978799863472,
          55.939373319824746,
          55.56802153118479,
          55.19274824341826,
          54.82516836484518,
          54.46036420260913,
          54.09312668068759,
          53.720602759993774,
          53.347141082355314,
          52.977217399313176,
          52.60544469504744,
          52.231245758458655,
          51.86262875506664,
          51.48958602472073,
          51.10815682545779,
          50.734183351549625,
          50.367506478884444,
          49.98626029194108,
          49.6205372239061,
          49.27001394314357,
          48.903551084548106,
          48.545840628233854,
          48.20572630638323,
          47.85017563444385,
          47.50203638598253,
          47.16189595676222,
          46.8105192683672,
          46.4616724198868,
          46.11675334786447,
          45.76150551370608,
          45.40480869765571,
          45.0564256342748,
          44.69301438476904,
          44.328669530061376,
          43.970718524939905,
          43.600648893620146,
          43.234265683391236,
          42.87335991012285,
          42.50779225583399,
          42.14136351297361,
          41.773998289621716,
          41.413963899819706,
          41.04360806681638,
          40.67227553532139,
          40.30534187909715,
          39.938583850157,
          39.57232258726005,
          39.20461295054296,
          38.84186948892558,
          38.4815026544245,
          38.11863754521617,
          37.71766328846792,
          37.364449059155376,
          37.00607120374936,
          36.64493000384855,
          36.293010597450625,
          35.939525769616345,
          35.5904616235215,
          35.24546513219415,
          34.894027191727304,
          34.549105368730565,
          34.21214441652453,
          33.860048232656354,
          33.506993469430085,
          33.173262668129574,
          32.81705216205169,
          32.455906030819726,
          32.1119529633496,
          31.76042768706502,
          31.392221451121877,
          31.04788433749136,
          30.70089819819073,
          30.336189436506217,
          29.985364833468218,
          29.64365077860534,
          29.289581901103503,
          28.94066344790009,
          28.60358170096688,
          28.25857592849617,
          27.910567763065607,
          27.567151212378207,
          27.22930915995325,
          26.883128163039142,
          26.53755015476938,
          26.202097147862276,
          25.861695991717816,
          25.520314020498144,
          25.188096392192843,
          24.860353423164398,
          24.526045586486205,
          24.190550145528015,
          23.858761824728827,
          23.520103726112797,
          23.171835358180676,
          22.83017504711984,
          22.485837478395712,
          22.136195057745407,
          21.790947699710443,
          21.439661254885042,
          21.083696979380083,
          20.729152384853908,
          20.373968406818832,
          20.0119016424376,
          19.65164263492593,
          19.299154643473575,
          18.933127191151954,
          18.567172565391644,
          18.203942620002955,
          17.82041076974728,
          17.44219721807595,
          17.066433865393208,
          16.67981266439099,
          16.299925036839067,
          15.921158900128974,
          15.535325581248024,
          15.159703687894108,
          14.778789360563444,
          14.38486600912855,
          14.018149681546012,
          13.64354128263099,
          13.24390955367839,
          12.871769614452925,
          12.498122272196419,
          12.102375483405968,
          11.717987764513454,
          11.341031861739433,
          10.94354944890784,
          10.562486265862209,
          10.211661168617892,
          9.850749834560679,
          9.493321670701118,
          9.147193298779058,
          8.792766806243337,
          8.435000983779947,
          8.08425470503224,
          7.725638548135348,
          7.367650831168109,
          7.001657342914041,
          6.626779304949715,
          6.2492442416911524,
          5.872324041868941,
          5.501708559410655,
          5.128360917396018,
          4.755126297768746,
          4.3848997099928075,
          4.017877371069346,
          3.646376893614569,
          3.2757738324049233,
          2.906398981568199,
          2.534818768370754,
          2.1627778091897523,
          1.7969270286896442,
          1.4380057167064924,
          1.0759154855397155,
          0.7200750159389558,
          0.37321479041646605,
          0.02914811308890497,
          -0.31084487447118736,
          -0.6411563408619088,
          -0.9700405069957634,
          -1.2968516204502167,
          -1.6187702029437863,
          -1.94924394322357,
          -2.280196630770843,
          -2.600157316472305,
          -2.960841026799311,
          -3.292736306607323,
          -3.6130130420295874,
          -3.9324589721138103,
          -4.2566077648040315,
          -4.569230536732782,
          -4.877077986532633,
          -5.194499418537056,
          -5.500649079211376,
          -5.7992824020769485,
          -6.107106154386381,
          -6.405171577397624,
          -6.695996081850355,
          -6.990106228515937,
          -7.2645641923146504,
          -7.536418918896798,
          -7.806437790192162,
          -8.055528415089872,
          -8.298830415702062,
          -8.542599043226232,
          -8.771534970970293,
          -8.99732734817232,
          -9.223156039062935,
          -9.444156429620103,
          -9.666449060639593,
          -9.879196217107502,
          -10.076953233068856,
          -10.268047652564398,
          -10.448530993608301,
          -10.620862636321968,
          -10.773007855871452,
          -10.90413711598579,
          -11.024395682413983,
          -11.12131767093289,
          -11.195311711290422,
          -11.257564571362938,
          -11.30554867383601,
          -11.334862831547248,
          -11.345610505732335,
          -11.335971282122784,
          -11.305315244874388,
          -11.254326853020563,
          -11.185334945115759,
          -11.098908981935024,
          -10.991857438779702,
          -10.867094453315586,
          -10.725895449337363,
          -10.565612729848949,
          -10.389309516606826,
          -10.181857961698018,
          -9.978157231422392,
          -9.75877894732609,
          -9.529303184775374,
          -9.287813591964635,
          -9.032844174721795,
          -8.770159377744065,
          -8.500939516158535,
          -8.221755519556217,
          -7.938159960585356,
          -7.648412131392705,
          -7.350297755837052,
          -7.05191260506969,
          -6.747764242693863,
          -6.4332160388749555,
          -6.119451080795939,
          -5.805630004632701,
          -5.453848208092183,
          -5.133743843150374,
          -4.813329377269034,
          -4.494614359040718,
          -4.177520454427168,
          -3.8555846546148986,
          -3.5392039734301997,
          -3.223142220419046,
          -2.9076650903579653,
          -2.5961477603127685,
          -2.2789353876814418,
          -1.9698300895897383,
          -1.6595802990074289,
          -1.3441143596696223,
          -1.0319385955766565,
          -0.7303708648775338,
          -0.4257343819453934,
          -0.11355873769257524,
          0.1848800796468899,
          0.48594135202888367,
          0.7807654884331111,
          1.0821147100280377,
          1.3871041777993764,
          1.673214114492387,
          1.966100598569601,
          2.2638067337789956,
          2.5456166530868902,
          2.8266206016463196,
          3.118014791034848,
          3.3980619553093994,
          3.6677763652226436,
          3.946345628878007,
          4.219737474503075,
          4.482193017474221,
          4.749661617988702,
          5.041937120542202,
          5.299879178200307,
          5.555825128889483,
          5.812391850943208,
          6.068196503660831,
          6.32281550630052,
          6.575297631144122,
          6.829924972350936,
          7.084858196225822,
          7.339981650440308,
          7.598041464755717,
          7.856545112144505,
          8.116685456238024,
          8.375691789472686,
          8.637395828400763,
          8.898571832320323,
          9.155551053943862,
          9.41437108513193,
          9.675681488936188,
          9.929339015685203,
          10.181109481421531,
          10.439739513296772,
          10.693531272221275,
          10.945431649953704,
          11.200342214580663,
          11.451931446830132,
          11.702806565882462,
          11.954600655223974,
          12.210912814967877,
          12.470629714020555,
          12.72515289627694,
          12.985583709935213,
          13.253058338559866,
          13.519215734229753,
          13.790686281091544,
          14.065600262647369,
          14.334390661359674,
          14.610560765833304,
          14.894901100692035,
          15.17442051311233,
          15.461168351372704,
          15.75923402742882,
          16.058283484698343,
          16.364850777698678,
          16.682641728470735,
          17.002094767420743,
          17.326480451301308,
          17.654470714292504,
          17.99275921647582,
          18.33065303775773,
          18.66789065502258,
          19.014426084696105,
          19.36238286110806,
          19.704622712487296,
          20.04782905101017,
          20.39807170399852,
          20.74648153364409,
          21.09667575382273,
          21.458376186852544,
          21.8154178775815,
          22.171981850202762,
          22.54102625495687,
          22.900840225382197,
          23.263486469752056,
          23.631912560010452,
          24.001278602969418,
          24.37123281051683,
          24.7469215559245,
          25.12101708519,
          25.49887012928312,
          25.876734331534657,
          26.251514829847398,
          26.631308113226876,
          27.01478272088062,
          27.39695444809838,
          27.78110199218448,
          28.17254613216134,
          28.569106724102877,
          28.961339627436082,
          29.35135558414037,
          29.749100074450322,
          30.14321972192303,
          30.52148331775037,
          30.912838854047582,
          31.309051754079654,
          31.691424831442735,
          32.08462793478433,
          32.48826967906086,
          32.88522327773766,
          33.280666398757916,
          33.69143051461729,
          34.09857635249731,
          34.495809284122906,
          34.90972755492537,
          35.32641800863097,
          35.726380578907765,
          36.131956109604666,
          36.54334045182919,
          36.93405689100981,
          37.33096345447413,
          37.73495854488367,
          38.12850926519715,
          38.51861270734441,
          38.91108642013776,
          39.29670465846797,
          39.672704604662584,
          40.05261378546899,
          40.43865700868703,
          40.81342358090363,
          41.1927947000017,
          41.57587892278698,
          41.93749766957197,
          42.29198412341117,
          42.64473959848332,
          42.99240438704664,
          43.31661455331717,
          43.64753312021521,
          43.9811848093274,
          44.29410966325423,
          44.61116345109599,
          44.925425524671525,
          45.26764747288758,
          45.63159911322485,
          45.987783056310484,
          46.34545024379717,
          46.70655364556542,
          47.060195150761096,
          47.4076211125713,
          47.77472973248199,
          48.11828680602984,
          48.46043676644089,
          48.795559069212345,
          49.09971632883479,
          49.41064145883806,
          49.730083158507405,
          50.02982309514541,
          50.330727559914244,
          50.64107993575205,
          50.93014156712458,
          51.22678746960409,
          51.531412154092614,
          51.81763255621389,
          52.12230758122566,
          52.434341496681384,
          52.73102397372358,
          53.04013513222913,
          53.34059037417727,
          53.618605490128516,
          53.90659760280088,
          54.192890790903306,
          54.45498188317695,
          54.70871464379646,
          54.95550652188816,
          55.183049012966066,
          55.40346651223312,
          55.62050662003525,
          55.82331803509388,
          56.016324483685715,
          56.20121427424938,
          56.37644610438219,
          56.546352990824865,
          56.70698258528733,
          56.855316132679235,
          56.997761037135625,
          57.13730842154169,
          57.27012624841349,
          57.39918845375359,
          57.523924552491216,
          57.646218279906286,
          57.76682881762626,
          57.87845154979485,
          57.98171683278338,
          58.0837930203256,
          58.180703875228225,
          58.27202527955494,
          58.3636526320031,
          58.45261810388046,
          58.53582866390415,
          58.61906585290884,
          58.70293991074844,
          58.78471591221687,
          58.86730692886669,
          58.95029758161424,
          59.031485447131544,
          59.11021138571174,
          59.18642734809558,
          59.260428315398634,
          59.33524061103537,
          59.40986068200712,
          59.48497563361193,
          59.563038262200706,
          59.64118904352176,
          59.719389227563056,
          59.79999744605393,
          59.88217153361043,
          59.964871410899896,
          60.05119441990244,
          60.137591677123176,
          60.22619471515172,
          60.318508430333836,
          60.40952165630987,
          60.50043222917768,
          60.5945583922765,
          60.68679686442921,
          60.778815804493554,
          60.872926974700064,
          60.96760948296921,
          61.06510027982875,
          61.163188489969684,
          61.25702503300955,
          61.349315056846976,
          61.44188562803304,
          61.527751759479266,
          61.61244873209348,
          61.69821207881477,
          61.77804468509739,
          61.85392699597834,
          61.9296259251221,
          62.00185851993849,
          62.07031203850655,
          62.13670537887578,
          62.1959730071792,
          62.252054615502345,
          62.30594724122542,
          62.354968908932186,
          62.40157162573766,
          62.446080474692295,
          62.48793407151723,
          62.528135959076735,
          62.56649463856644,
          62.602434624261974,
          62.63605204349345,
          62.67193698824227,
          62.7030455772307,
          62.73310789095448,
          62.76261250005511,
          62.79090938588217,
          62.818936450635455,
          62.845163302784016,
          62.8695290224375,
          62.892292289603034,
          62.912795979382366,
          62.93276787448488,
          62.951547733171196,
          62.96930952381978,
          62.985908338554886,
          63.00100839521937,
          63.01491422169226,
          63.029392089035795,
          63.043274882227536,
          63.05896518683577,
          63.07471420229797,
          63.091320673777,
          63.109982962561546,
          63.128254780772394,
          63.14753697128567,
          63.16757708753383,
          63.18851365896184,
          63.20761823645554,
          63.224094590590525,
          63.235655279438106,
          63.23870598354821,
          63.233969492609766,
          63.22170615467716,
          63.20163108773384,
          63.171795011999365,
          63.133420056463805,
          63.084749435676436,
          63.025458453939386,
          62.95380604453136,
          62.86446133042564,
          62.75632565721195,
          62.63288671535663,
          62.4917398965239,
          62.336809315963485,
          62.16553558828467,
          61.97675291774159,
          61.77291507890253,
          61.54716385384834,
          61.30276804090229,
          61.04906636793197,
          60.81192018532945,
          60.56260959142985,
          60.29807756051385,
          60.02735269771747,
          59.75756439150738,
          59.47018141777021,
          59.18461171782139,
          58.90238529591176,
          58.614051219608356,
          58.3138527602646,
          57.98987137159376,
          57.66113841023117,
          57.32528506035067,
          56.97945762935523,
          56.624291519878994,
          56.26690719973818,
          55.901062792314356,
          55.52552192809759,
          55.144598532642135,
          54.76773163315791,
          54.38781787880138,
          53.99855289255219,
          53.625743133069726,
          53.2475060155093,
          52.862831946016485,
          52.49345287559652,
          52.124271896562554,
          51.74727760748255,
          51.38079460569861,
          51.01246481029312,
          50.6327046425791,
          50.26711932774592,
          49.90888746479829,
          49.53182921533975,
          49.179061853261985,
          48.837956607367765,
          48.47663391855183,
          48.13339849572884,
          47.807130651350334,
          47.46060498414247,
          47.13047961357537,
          46.81050199965301,
          46.48116377776248,
          46.15517677256216,
          45.83336861948094,
          45.50583457082173,
          45.17456112370085,
          44.85502704005448,
          44.52374282985643,
          44.186904996750734,
          43.851592128623814,
          43.511495011844005,
          43.16579926367237,
          42.8259385661728,
          42.487421675428635,
          42.14539076670972,
          41.808687079462835,
          41.46479020081303,
          41.130959931063494,
          40.788691585847054,
          40.44887466649771,
          40.10927829772693,
          39.77002482148344,
          39.43485072208063,
          39.093569581347964,
          38.75302585523253,
          38.41412028805515,
          38.07120754858951,
          37.72757880701141,
          37.38312390395235,
          37.04339759063215,
          36.69508614787157,
          36.345535567599875,
          36.00737759443102,
          35.663580378106325,
          35.32349665479488,
          34.99210119425043,
          34.656152584047234,
          34.32288104240155,
          33.99827326290476,
          33.66638131292083,
          33.31999482143221,
          32.99295440893254,
          32.66735726284639,
          32.31820279224586,
          31.985899408158176,
          31.659437313613736,
          31.31880198601785,
          30.983438920063314,
          30.660649658063626,
          30.33365059744347,
          30.000866297226633,
          29.677988482754955,
          29.351699464293194,
          29.025146253227067,
          28.695054930418227,
          28.370034291751537,
          28.04320686008069,
          27.711887811765415,
          27.375061413167217,
          27.040921969547455,
          26.702907940340957,
          26.35139220415963,
          26.010598618440127,
          25.671114492553663,
          25.33059340504493,
          24.985079994070087,
          24.652816454680803,
          24.322710260057878,
          23.988332825446566,
          23.661986743018332,
          23.33595772102648,
          23.007365920352882,
          22.67609709624427,
          22.34821549841634,
          22.017152230876107,
          21.684010531005494,
          21.361914949505756,
          21.02906773489013,
          20.694940535120928,
          20.378817997334668,
          20.059647697944126,
          19.742853954303467,
          19.42372570966386,
          19.102934200679478,
          18.782781053885877,
          18.461994721161368,
          18.134255251297347,
          17.805967472141052,
          17.47281580815261,
          17.135381320577427,
          16.791744922108798,
          16.444079608910577,
          16.105995807866144,
          15.760409508327378,
          15.41407709316523,
          15.076647029920318,
          14.734190441943847,
          14.375625391305734,
          14.03758728061147,
          13.70184017889557,
          13.333255814926211,
          12.983241297030743,
          12.645480373088091,
          12.28193083004375,
          11.925467495779497,
          11.577256488612214,
          11.217164940611902,
          10.854636258351285,
          10.499137907620133,
          10.137277040644857,
          9.772402009631524,
          9.41340352889663,
          9.047990871382273,
          8.68358350029497,
          8.317308092290189,
          7.949508399718211,
          7.577362602041926,
          7.207065092168341,
          6.833096390969102,
          6.456403504196448,
          6.081422938363752,
          5.6993800241452375,
          5.322112442291334,
          4.9422177586188925,
          4.558682149708401,
          4.1759764551250615,
          3.793614633532611,
          3.4095077825844093,
          3.021632790120178,
          2.6386464893866926,
          2.260961565749568,
          1.8768156788892656,
          1.494776247195664,
          1.1237720527434525,
          0.750241881576778,
          0.3644939115835353,
          0.0003985413238350999,
          -0.36358758444680306,
          -0.7339211116538464,
          -1.0944189240434319,
          -1.4485512442573514,
          -1.8000793387959915,
          -2.154012506924186,
          -2.5101263575659245,
          -2.856845843226264,
          -3.203570454917672,
          -3.5591999394454676,
          -3.9054885234646655,
          -4.241166831409329,
          -4.597008179585605,
          -4.938465526157004,
          -5.262236639455328,
          -5.606329825662732,
          -5.950955584231887,
          -6.273702279706305,
          -6.610493222183457,
          -6.94071855056408,
          -7.260365747155487,
          -7.593618122696932,
          -7.892163121286971,
          -8.18627500426156,
          -8.491631030293615,
          -8.771412568717908,
          -9.038346341614425,
          -9.309063432433401,
          -9.562449417428644,
          -9.804035582156809,
          -10.04283045296987,
          -10.268579233684013,
          -10.482590142379573,
          -10.692718389030276,
          -10.894029361453741,
          -11.082637687465967,
          -11.261804939941495,
          -11.430246541106198,
          -11.587534568944571,
          -11.729897448269384,
          -11.854485351357262,
          -11.963264935204627,
          -12.05246316171118,
          -12.118558364809497,
          -12.164869482562567,
          -12.189130725413053,
          -12.191962098734965,
          -12.172762375102891,
          -12.132524787942378,
          -12.071756574667436,
          -11.987976332305832,
          -11.881197911663184,
          -11.753366259590033,
          -11.60717323003133,
          -11.437445332374683,
          -11.247192511763327,
          -11.038114118134464,
          -10.809118261493788,
          -10.567216774687227,
          -10.315191112009325,
          -10.046424754158279,
          -9.764175592237091,
          -9.474437967949074,
          -9.17042074704547,
          -8.824884232635538,
          -8.507898210986419,
          -8.182792298142976,
          -7.854943463752893,
          -7.524013289983076,
          -7.189469816086135,
          -6.858392215792005,
          -6.522374038079284,
          -6.184604798517509,
          -5.8486399555739315,
          -5.50980696830572,
          -5.170810860163108,
          -4.832505029669365,
          -4.4966380160899915,
          -4.161232258298383,
          -3.8238912928848556,
          -3.4897011370596083,
          -3.154191311839693,
          -1.9737318427051402,
          -1.6385391859771126,
          -1.3002215533887205,
          -0.9630799955640327,
          -0.6356851791594373,
          -0.307764297562342,
          0.024012512080520465,
          0.3414866463822026,
          0.6545461276978739,
          0.9632812372732267,
          1.2842463641676103,
          1.5950713413832374,
          1.891069559661427,
          2.2016936967191065,
          2.506943151730935,
          2.79764489119945,
          3.0967509811087672,
          3.3992660380833524,
          3.684146787958361,
          3.971970866198464,
          4.26742962751653,
          4.5489891462046295,
          4.8322019951504664,
          5.1200867715042,
          5.398035224886245,
          5.67328487536808,
          5.950327825487951,
          6.230058613141949,
          6.506658642707398,
          6.7811784829935435,
          7.0579095864872645,
          7.33456036649446,
          7.609245833004409,
          7.888440785146189,
          8.16775389894576,
          8.446902979043847,
          8.727087537616262,
          9.010143277063444,
          9.290403626206134,
          9.568224255375616,
          9.849845092091241,
          10.1307202506979,
          10.403706081597347,
          10.680476080620002,
          10.9625292292068,
          11.23648399879197,
          11.513661240099827,
          11.792487271740285,
          12.069717001604555,
          12.346867083314574,
          12.632405499810076,
          12.922026735659495,
          13.2069000058912,
          13.502272801566226,
          13.80449773840674,
          14.10463318696719,
          14.411123877948137,
          14.716847300164286,
          15.01772420836033,
          15.328457788309667,
          15.640121931645558,
          15.953731111737216,
          16.2824006428232,
          16.615693116438134,
          16.95270320722105,
          17.302864723360862,
          17.65573322551638,
          18.008482388213544,
          18.36665727974754,
          18.73189700118935,
          19.088133894567918,
          19.451082926110107,
          19.81995209976455,
          20.179114721815864,
          20.535434180325428,
          20.8983707253235,
          21.261541890376268,
          21.61281452399978,
          21.963886782965623,
          22.314933020785375,
          22.660123067030305,
          23.014022588880138,
          23.393473736406502,
          23.738104036360916,
          24.087768581149984,
          24.435201541277188,
          24.7824500190354,
          25.141564869019163,
          25.504081536225755,
          25.86615912699942,
          26.232462113011955,
          26.591296082660524,
          26.95045571710823,
          27.311673803146704,
          27.670899872623043,
          28.033469254476483,
          28.395852571991693,
          28.753774740279187,
          29.106318672094904,
          29.45465755315703,
          29.802844724543828,
          30.152908814015888,
          30.503525446701126,
          30.84279161926177,
          31.182376399200262,
          31.532104117487183,
          31.875105262532564,
          32.21885387849948,
          32.57907926851076,
          32.94231376733323,
          33.30151913415881,
          33.659118712600886,
          34.02475940265809,
          34.38919311999698,
          34.74656831143345,
          35.10797829610265,
          35.47350575426272,
          35.834912568002814,
          36.19424489417513,
          36.5540653260781,
          36.911152798106926,
          37.26325471497696,
          37.60901900683631,
          37.956517716861924,
          38.30472036872867,
          38.64699233524936,
          38.98316056813063,
          39.32090458742762,
          39.65797964012224,
          39.986538965712995,
          40.311786431913724,
          40.64233160779546,
          40.972222121131104,
          41.298964887565184,
          41.62993903784697,
          41.96672059886023,
          42.29677412252249,
          42.61986524652843,
          42.94138147128926,
          43.26574115153405,
          43.59179284992204,
          43.900353090044746,
          44.22344286570073,
          44.54930420767907,
          44.864903689150474,
          45.18420711455336,
          45.49969274010402,
          45.81512917397828,
          46.13584710069355,
          46.44733423181216,
          46.76220208799387,
          47.076807981698416,
          47.382076065757346,
          47.688806309722004,
          48.00442256531817,
          48.292607069219116,
          48.593730951703755,
          48.899864756455,
          49.1925564533268,
          49.4991376773186,
          49.79782814085616,
          50.08316079673435,
          50.379642796385134,
          50.66860915344607,
          50.94589924954362,
          51.23773510837194,
          51.518432553090456,
          51.793116339138074,
          52.08706940377377,
          52.37097901113291,
          52.65383574061299,
          52.94443050456713,
          53.21341918663115,
          53.47068292800913,
          53.73884723518855,
          53.996471347978506,
          54.23767144868568,
          54.48282433504803,
          54.720611058513306,
          54.94401215399161,
          55.16382514437546,
          55.3768715664172,
          55.580756052840634,
          55.77909951804382,
          55.969507456717686,
          56.155881026108496,
          56.33948246819552,
          56.5161142029926,
          56.68125300566708,
          56.842342615480625,
          56.999093377325856,
          57.14716472899634,
          57.288858847494616,
          57.426220120422165,
          57.56270789814683,
          57.69536873625203,
          57.818045539406576,
          57.93343194193157,
          58.048467410144085,
          58.157744944336095,
          58.26230734617762,
          58.36832211829607,
          58.470997291306155,
          58.5681774612219,
          58.667291050790496,
          58.76832674550958,
          58.86706566241966,
          58.968086576631144,
          59.071374491239226,
          59.17335319888448,
          59.274612249440175,
          59.37575831482317,
          59.47451892877917,
          59.57455920261261,
          59.675472399878764,
          59.77330548291015,
          59.87071791706412,
          59.96739275776205,
          60.06244165708001,
          60.15531053455021,
          60.24892509758613,
          60.34125835131264,
          60.43449433922638,
          60.52684563408207,
          60.61788529151114,
          60.710231249883186,
          60.802531957020676,
          60.89229565968945,
          60.98364618799147,
          61.075344749079385,
          61.16267403481749,
          61.25099316157184,
          61.33769375279625,
          61.418371415806654,
          61.49886545283948,
          61.57946770113693,
          61.65534421255556,
          61.72932788793069,
          61.80529134523092,
          61.88113926562536,
          61.952468600354884,
          62.025018703511805,
          62.09757486678338,
          62.16739706332694,
          62.23525307390041,
          62.30380653146329,
          62.37119854336666,
          62.43841707233342,
          62.505455562680034,
          62.56953399713478,
          62.629853184173896,
          62.69007172836357,
          62.74913967076412,
          62.805214306062396,
          62.860767487516306,
          62.91504266123033,
          62.966751746810516,
          63.017817537026566,
          63.067214910558434,
          63.1145316734767,
          63.160261658140854,
          63.20302685052921,
          63.24439547293186,
          63.285078147137455,
          63.32464416443559,
          63.36378760992091,
          63.402003962270605,
          63.4409601578963,
          63.47927263730376,
          63.516952602389274,
          63.55546472979714,
          63.59366697584465,
          63.63179518795001,
          63.668400506018685,
          63.702777610892625,
          63.73541358316437,
          63.76707001065267,
          63.796620918936085,
          63.82288155468991,
          63.84869527026163,
          63.87444941905167,
          63.90034133648056,
          63.92404792968703,
          63.94650694364895,
          63.96913409079851,
          63.98982060470319,
          64.0093302322701,
          64.0286271966915,
          64.0473146786593,
          64.06248738416762,
          64.07402740341747,
          64.08002180612183,
          64.07659962763822,
          64.06384040676674,
          64.04279999167841,
          64.01591457120747,
          63.981901711643054,
          63.93830113197171,
          63.88432825143542,
          63.82110130817472,
          63.74144488631624,
          63.64991395774259,
          63.54982046129109,
          63.43423524800037,
          63.31195682136455,
          63.179859981281865,
          63.03251568845554,
          62.873890024259914,
          62.70273104787438,
          62.51344950987808,
          62.31450843931211,
          62.10732110698419,
          61.87820412792564,
          61.63588581346066,
          61.3847033016833,
          61.11810205098032,
          60.83706638036837,
          60.55203503960896,
          60.2591233378391,
          59.948951560720836,
          59.64281947898163,
          59.33516076505868,
          59.004243035341744,
          58.667274938813655,
          58.34273001607041,
          57.994636080939785,
          57.64120466906325,
          57.29364517337805,
          56.93426079697316,
          56.556660529239416,
          56.18403017854882,
          55.80900449570857,
          55.41917603594155,
          55.02937074627333,
          54.64668410989559,
          54.263856088877475,
          53.87902730349544,
          53.493855497489264,
          53.11790955051931,
          52.74745688527212,
          52.377430646436544,
          52.00596605767546,
          51.642450941617355,
          51.276010578250194,
          50.90592467610153,
          50.54444678464213,
          50.18869726716759,
          49.81958842033298,
          49.46563725991618,
          49.12457225145264,
          48.769088141286524,
          48.42062152718872,
          48.08871152984518,
          47.7424664506105,
          47.39875944077264,
          47.06572009332854,
          46.723479088438125,
          46.359131743290476,
          45.986169541620534,
          45.60580434355666,
          45.21941283139749,
          44.84368944054191,
          44.459233632677716,
          44.06626309643785,
          43.678532573836115,
          43.28945541800294,
          42.89309493447638,
          42.52171615307756,
          42.16496809230723,
          41.80526766013752,
          41.45012656547276,
          41.09094409781602,
          40.73883385461795,
          40.37823207683645,
          40.01556331005153,
          39.65527860386862,
          39.2946882258996,
          38.9221253452897,
          38.53544198257951,
          38.15137565783821,
          37.77096038937727,
          37.38378573234496,
          37.00115849769297,
          36.62009551481536,
          36.24490909142492,
          35.86053987428015,
          35.479430322576235,
          35.12068256213927,
          34.76594592787762,
          34.41818353302561,
          34.074535796423135,
          33.724472684194104,
          33.38380537361463,
          33.0496550609126,
          32.70537985536714,
          32.358402812894454,
          32.03367477796552,
          31.725437651837435,
          31.42617294459622,
          31.149074929892038,
          30.871568882677945,
          30.581436281530905,
          30.306547390480556,
          30.04087091043798,
          29.76012651411064,
          29.483645071357614,
          29.21307170943519,
          28.915186308402184,
          28.604167477899512,
          28.288628513693478,
          27.977575436308996,
          27.666749410052798,
          27.351455150869977,
          27.031084307673783,
          26.71936963476472,
          26.4097667489724,
          26.082145734507638,
          25.773228112565835,
          25.475845342097497,
          25.17623792187484,
          24.87266148744582,
          24.57485526049901,
          24.28284714423407,
          23.984346432486845,
          23.688828093892848,
          23.385733891422916,
          23.079637227283133,
          22.75973774823947,
          22.431820054580353,
          22.106285926365747,
          21.77078716473946,
          21.438052313008484,
          21.108643319797075,
          20.77109786837603,
          20.434946040825935,
          20.097575044871853,
          19.755615424501208,
          19.421709829416844,
          19.07805445042185,
          18.730357425605046,
          18.392039300055664,
          18.04775191546549,
          17.694706556844277,
          17.349081231626972,
          17.003669784259788,
          16.647475010543413,
          16.294823821546398,
          15.95004523550347,
          15.590401465404417,
          15.241476400933735,
          14.896275917120366,
          14.541738143053328,
          14.176568671082565,
          13.833629669157414,
          13.4877111984884,
          13.11209533932878,
          12.765639870716381,
          12.409852160708132,
          12.030519169784274,
          11.662935647236951,
          11.29781739679997,
          10.923576480105778,
          10.547104620491362,
          10.179325940711486,
          9.80434720851576,
          9.429431366182074,
          9.059660224708054,
          8.69054853623304,
          8.324308983430388,
          7.958635966271055,
          7.592422218232839,
          7.219580964664512,
          6.85391204688046,
          6.481846032388735,
          6.113956451600927,
          5.746893148429063,
          5.3738508094908966,
          5.007064243172127,
          4.640787405981305,
          4.266990967158904,
          3.8950800310339235,
          3.5254868278999685,
          3.1530785584810084,
          2.7745049887310405,
          2.4031625463945376,
          2.0358503048240895,
          1.6602091810320045,
          1.2866470989772245,
          0.9253257759194027,
          0.5660115461467957,
          0.1947891702247525,
          -0.15397659762822646,
          -0.4983643907005726,
          -0.8525912938512082,
          -1.190695290075616,
          -1.5265366704449703,
          -1.86635950314589,
          -2.205113876403413,
          -2.546212473323805,
          -2.8910134919435793,
          -3.229743424973572,
          -3.5765738944320233,
          -3.924473354456995,
          -4.261422577449902,
          -4.614755685900284,
          -4.956168369049133,
          -5.289259111332057,
          -5.630929687233937,
          -5.964512369533704,
          -6.287819979380584,
          -6.609399078478686,
          -6.928382847656105,
          -7.2375223397370885,
          -7.546363982114743,
          -7.841229940460219,
          -8.126118350021194,
          -8.41201674665735,
          -8.683967032550587,
          -8.946428999248381,
          -9.208739878809554,
          -9.462449244669466,
          -9.70802138855128,
          -9.946431884395997,
          -10.179279382753352,
          -10.405321405135073,
          -10.62507300362832,
          -10.836118675686093,
          -11.037670172389538,
          -11.22931187704759,
          -11.406259548666682,
          -11.572792775313768,
          -11.724318105319606,
          -11.850917331391768,
          -11.953485160141375,
          -12.037361516674807,
          -12.097391138291137,
          -12.133227296558076,
          -12.147547885513015,
          -12.14006660237752,
          -12.111208670075818,
          -12.058593481029705,
          -11.981601836514225,
          -11.880140002609227,
          -11.757401062127498,
          -11.610686807803447,
          -11.4412308739108,
          -11.251774504910673,
          -11.039699254475883,
          -10.81315614756676,
          -10.573723007639135,
          -10.318117403544377,
          -10.04776067425619,
          -9.768494126980976,
          -9.476561592617353,
          -9.173701308180583,
          -8.86204466143557,
          -8.540913147582616,
          -8.214752736638937,
          -7.882719101297022,
          -7.5446705883891445,
          -7.208515508164834,
          -6.8660881419934165,
          -6.520255981065731,
          -6.17761044765736,
          -5.830993800361853,
          -5.481652060542046,
          -5.135176310518312,
          -4.7935572385906084,
          -4.420157076347853,
          -4.081138504039376,
          -3.7480614424401693,
          -3.416683568894925,
          -3.0866646700464693,
          -2.7582059205503073,
          -2.428680949195049,
          -2.1009562566269633,
          -1.7753578176490288,
          -1.4465325729677032,
          -1.1231669232756571,
          -0.8067701258043809,
          -0.48370082569399264,
          -0.16769986167306367,
          0.1451894369885438,
          0.4535405492032794,
          0.774943946132012,
          1.0872690449768723,
          1.3852465568904504,
          1.700348673591054,
          2.010794353926612,
          2.307851899755635,
          2.6146603307090945,
          2.9251205363825696,
          3.218847870114183,
          3.5189409669088203,
          3.8216973438900106,
          4.112045409085448,
          4.407418879691832,
          4.701849051475603,
          4.984908571612931,
          5.267735812588464,
          5.555947167319271,
          5.837924725715278,
          6.115309628035547,
          6.3973571694964235,
          6.6796926940459445,
          6.957475656784271,
          7.240111295023662,
          7.526943558446389,
          7.812566779546011,
          8.098813056052256,
          8.389093241211894,
          8.675448464599093,
          8.959908552629726,
          9.249561132054787,
          9.531362916679806,
          9.80930281397461,
          10.09680498468821,
          10.379857955303388,
          10.65987416102991,
          10.94550052063651,
          11.233213006933104,
          11.516749345803488,
          11.807598814861917,
          12.105316539300597,
          12.397904728931232,
          12.698608826519814,
          13.036461936633428,
          13.340525748616427,
          13.650228885451888,
          13.958421377134563,
          14.266513153286832,
          14.579031386588914,
          14.892473484213435,
          15.21520906247777,
          15.546890816370478,
          15.87688046768632,
          16.218917749749462,
          16.571873797087093,
          16.919927397179663,
          17.267370962628103,
          17.62829709758554,
          17.982281450383365,
          18.333048093511373,
          18.695792703167193,
          19.054039015790117,
          19.399965811812052,
          19.753101088424188,
          20.11710475903152,
          20.468904903706072,
          20.83096264184473,
          21.199402163121455,
          21.56266363500743,
          21.92694427097784,
          22.296374902080235,
          22.65840419189045,
          23.02344377997737,
          23.389167695567007,
          23.75545997424605,
          24.121720005111438,
          24.489980522115406,
          24.856307937139775,
          25.227080510221093,
          25.59362096993688,
          25.95773426957631,
          26.326110032938168,
          26.692752133667813,
          27.060702097660787,
          27.43017958349347,
          27.803788210660944,
          28.178526286266035,
          28.55166991805745,
          28.92343631307273,
          29.299377923421208,
          29.67307358882372,
          30.03479181254738,
          30.404678196397786,
          30.78183326366769,
          31.181878292729593,
          31.550363409317743,
          31.93092223212536,
          32.30652392097987,
          32.67565231571263,
          33.05489198021725,
          33.43671800031759,
          33.808555633598,
          34.18322179631348,
          34.56419436743094,
          34.93726239722992,
          35.307625422191144,
          35.677443536753614,
          36.04553293088179,
          36.408704500576086,
          36.76691273206612,
          37.12789688860783,
          37.48933793544555,
          37.84095834791005,
          38.190896365890865,
          38.582773265874806,
          38.93203951531471,
          39.274042532265845,
          39.62231096192946,
          39.9720781761825,
          40.31968433298482,
          40.66959107610259,
          41.026548389147635,
          41.3778024857211,
          41.72225025845963,
          42.06229157401763,
          42.40974953285443,
          42.751621699956935,
          43.080787822582,
          43.42690167768115,
          43.76855703310241,
          44.10479228063313,
          44.440915959201,
          44.77431337359457,
          45.10662851386231,
          45.46094619120686,
          45.808342695585985,
          46.15975171217776,
          46.506315606348885,
          46.844078813241644,
          47.19322510494851,
          47.515266626471785,
          47.84670460256572,
          48.18191510737193,
          48.50381769766905,
          48.81466401158964,
          49.11401632061397,
          49.403317735523665,
          49.70326838030182,
          49.99350772715099,
          50.27664946918454,
          50.574009520554895,
          50.856127445613495,
          51.13563734988419,
          51.43100948252961,
          51.71024698691648,
          51.995041528716584,
          52.2828001245033,
          52.543999734477055,
          52.79818063393478,
          53.062833429930436,
          53.31603947627008,
          53.5513319686284,
          53.790476856280144,
          54.02128608025901,
          54.24484994796885,
          54.46278214766334,
          54.671946921444174,
          54.87010320200749,
          55.05981263720886,
          55.23892510914591,
          55.409239038933634,
          55.57628863237356,
          55.73512105855887,
          55.88312969636046,
          56.037601843785545,
          56.18883410184367,
          56.33116699255883,
          56.46760413259681,
          56.59790203899644,
          56.72495218899766,
          56.85380808523675,
          56.975184052245204,
          57.09142895916407,
          57.20426547039739,
          57.310540910036146,
          57.41370663231651,
          57.51538703476197,
          57.61742164489792,
          57.71561049045584,
          57.81201532446704,
          57.91116592490751,
          58.011422147909336,
          58.11068680342482,
          58.21220435793892,
          58.31522108255103,
          58.418442245193724,
          58.52105016626588,
          58.62400693566569,
          58.7250857106172,
          58.82750827951949,
          58.93101737692925,
          59.032590191622816,
          59.1339849327446,
          59.235384220430845,
          59.33631552578168,
          59.43574142362113,
          59.535779689522975,
          59.64500019523664,
          59.744836338341294,
          59.842736860445015,
          59.93816991984187,
          60.032897376559305,
          60.12473050145164,
          60.2124355964005,
          60.30097411514164,
          60.3873991649243,
          60.46803999003559,
          60.550004255285856,
          60.6301685483377,
          60.7040459447709,
          60.7784767488248,
          60.85417969709186,
          60.9276451685494,
          60.99980458984615,
          61.071522607718556,
          61.14417113005666,
          61.219322102440415,
          61.29096448216104,
          61.360927914315965,
          61.4341652842808,
          61.505068575542055,
          61.57289079132632,
          61.64030095303006,
          61.70571420281428,
          61.76912038039181,
          61.83250286637176,
          61.89463014528182,
          61.95143213143881,
          62.007336552737364,
          62.06335851195561,
          62.11710249448164,
          62.168773601698476,
          62.220483847542305,
          62.26979688580645,
          62.318384438452625,
          62.36678070723835,
          62.41410722291134,
          62.460758185586684,
          62.50550431651555,
          62.54984886165757,
          62.5934387022575,
          62.63681602675735,
          62.68027596955813,
          62.7235165704154,
          62.76658786753604,
          62.809537712329906,
          62.85219241103102,
          62.89579581765202,
          62.93877130776275,
          62.980085827608356,
          63.01933518024041,
          63.056670212543544,
          63.092758501150115,
          63.12530266204414,
          63.15499639291959,
          63.18495235437026,
          63.21425369132545,
          63.24276248105419,
          63.26959046188912,
          63.29614862701168,
          63.32094853470265,
          63.342821015002045,
          63.36247286048999,
          63.381113352907896,
          63.39559935579364,
          63.4069544812618,
          63.41464804030659,
          63.41553550559999,
          63.40804107192399,
          63.39187460734041,
          63.36740745068784,
          63.334509840312606,
          63.29559094073917,
          63.249253431392745,
          63.195464350706004,
          63.134319662336736,
          63.05950820059209,
          62.97197680453213,
          62.87605146515514,
          62.76589256673009,
          62.64607750835021,
          62.519256160605494,
          62.37833259911176,
          62.22200641190058,
          62.05437435134139,
          61.87094591087604,
          61.67387044530865,
          61.47487611204491,
          61.259381666821334,
          61.02421136780594,
          60.78382551403607,
          60.53201503761655,
          60.266923094640035,
          59.99175650230652,
          59.71330163664198,
          59.42358865267714,
          59.12095716488916,
          58.829465736798284,
          58.525738793353874,
          58.19957422235465,
          57.883692342574726,
          57.56468454713975,
          57.220189492809055,
          56.883718281401364,
          56.54346139561328,
          56.19058480752353,
          55.82890053225424,
          55.46851848470298,
          55.10164367346424,
          54.72723891690356,
          54.35637953066699,
          53.98522439163164,
          53.61728799423,
          53.24664548859881,
          52.871031989161175,
          52.497065621641994,
          52.12881950173182,
          51.75679706051156,
          51.38211768770357,
          51.01719823254678,
          50.64654502135135,
          50.26738345506349,
          49.895512985789246,
          49.53345190249438,
          49.17047924444769,
          48.81407677580592,
          48.47413449100175,
          48.12799927402099,
          47.77831493568805,
          47.44929499195971,
          47.114600336976636,
          46.775184081547565,
          46.45143781016481,
          46.12032014097613,
          45.77953445033482,
          45.44804795964565,
          45.108872168663865,
          44.76423894352988,
          44.42513789819475,
          44.0862473496595,
          43.73504441833441,
          43.38793249611571,
          43.04378390555962,
          42.68951428160363,
          42.34454641705418,
          42.00420293947376,
          41.661184645138384,
          41.32038723498097,
          40.97837013283119,
          40.63649447577548,
          40.30005306001455,
          39.955183111636096,
          39.612556261236584,
          39.270990312134,
          38.92871827550783,
          38.58766717483126,
          38.24539001260121,
          37.90590095785497,
          37.56488989454538,
          37.22471904645714,
          36.883129955754804,
          36.54360508713182,
          36.174200328018145,
          35.83846948748642,
          35.52263117867542,
          35.20928432755148,
          34.89472508837139,
          34.58717727219647,
          34.27577478710454,
          33.96028078619159,
          33.656393101388375,
          33.35125219401434,
          33.03503564062306,
          32.71402241803113,
          32.39811779029053,
          32.06878705847447,
          31.724016816164948,
          31.400510017562983,
          31.077360952642394,
          30.74206556774704,
          30.41713643667577,
          30.105490155339325,
          29.78995024060322,
          29.471923274046212,
          29.17887591341842,
          28.88386513040068,
          28.59463801367735,
          28.30362591585875,
          28.010759354391112,
          27.72652510242391,
          27.440972500198153,
          27.150589205568867,
          26.861112483725588,
          26.579060996421017,
          26.277706763108057,
          25.966240397912934,
          25.670134418173415,
          25.371371672587152,
          25.074535109157953,
          24.777970317510672,
          24.482322071433558,
          24.19536270629075,
          23.903390143250498,
          23.614795122863292,
          23.320471315145653,
          23.023878300246846,
          22.72756634988025,
          22.424149403454845,
          22.122413473384118,
          21.817985269867396,
          21.50691703044525,
          21.202369412985476,
          20.89370456908331,
          20.571532633005138,
          20.25669443070181,
          19.938851502163917,
          19.612679927434932,
          19.289613832044996,
          18.959568853554533,
          18.632076621377326,
          18.2990021641359,
          17.960528193336145,
          17.621018854283523,
          17.271625409828836,
          16.920712917607652,
          16.574009682210736,
          16.21647818063653,
          15.85707275970383,
          15.508918724821502,
          15.147679745181923,
          14.787002438138943,
          14.43920787628254,
          14.071234177125318,
          13.70121492837306,
          13.352430513109278,
          12.981205153702996,
          12.600208273152308,
          12.243284342932425,
          11.87373390693562,
          11.491377337532775,
          11.12234811865268,
          10.751762284048406,
          10.363468548624388,
          9.985834010670732,
          9.609833523832139,
          9.182118154976337,
          8.800749782509422,
          8.422753380660426,
          8.038101562884759,
          7.6532280665617565,
          7.273715753938879,
          6.885858079780781,
          6.5060941357564435,
          6.123356359182788,
          5.736088139167882,
          5.348443740434719,
          4.962594126544416,
          4.579245000671015,
          4.193447609052545,
          3.8072503171656864,
          3.425665742939745,
          3.0435922483278706,
          2.658170011828071,
          2.275281716611861,
          1.8999890526239773,
          1.5210622922455812,
          1.14663090463916,
          0.7742754514835176,
          0.40107664980557045,
          0.029681644600288548,
          -0.3375242291933822,
          -0.7028733736258722,
          -1.0732581212481862,
          -1.4331811266702945,
          -1.7904946565320976,
          -2.1451324583006004,
          -2.497803521150139,
          -2.8503835368231774,
          -3.194247338562687,
          -3.5389898385324794,
          -3.8848295469978393,
          -4.2292078205621,
          -4.5643403234788416,
          -4.902665704726873,
          -5.2276636048163585,
          -5.535170021196102,
          -5.850088807595772,
          -6.175451794889589,
          -6.490853013774716,
          -6.7988372140586835,
          -7.122367251740657,
          -7.436068606666205,
          -7.738802645661212,
          -8.058399769177601,
          -8.375578011371097,
          -8.680409821592939,
          -8.990697894762434,
          -9.281158435043855,
          -9.55993118367805,
          -9.841602130141302,
          -10.113998451079441,
          -10.37716774491123,
          -10.6364891967188,
          -10.881568979445975,
          -11.114003490277911,
          -11.33980081487278,
          -11.554208799752875,
          -11.765195615113322,
          -11.9695233647449,
          -12.160861718609366,
          -12.341040433527219,
          -12.510037517159404,
          -12.662400773404304,
          -12.795279434582298,
          -12.909618821637794,
          -13.003301468671635,
          -13.070831645924557,
          -13.114504403662622,
          -13.135191530377767,
          -13.131422865659708,
          -13.10440465335795,
          -13.053012216564387,
          -12.978458620578525,
          -12.87795730558982,
          -12.755289034242294,
          -12.615325071788435,
          -12.45223498061398,
          -12.267184377297351,
          -12.069759167457331,
          -11.855477485909732,
          -11.624536527858567,
          -11.386480230515378,
          -11.135352927495594,
          -10.868062423603151,
          -10.593086987169931,
          -10.307467506183428,
          -10.009868595637103,
          -9.706427327421112,
          -9.39458778062222,
          -9.077600195467477,
          -8.755615634299993,
          -8.427476673356207,
          -8.098039874970743,
          -7.76305834477517,
          -7.417184262657636,
          -7.070243305740809,
          -6.723813539134538,
          -6.372553053415411,
          -6.018511449792451,
          -5.667633752166593,
          -5.319108153797582,
          -4.965128321716547,
          -4.615845657752876,
          -4.266784506746329,
          -3.909442032206474,
          -3.5574691551888336,
          -3.2035921575796356,
          -2.8522142286154786,
          -2.504641409065519,
          -2.1561305486307263,
          -1.8123236764333392,
          -1.4788333507227696,
          -1.1386033911629663,
          -0.8091393293994319,
          -0.49301161598759924,
          -0.18270464766558236,
          0.13770503153790448,
          0.4524245561292514,
          0.7470438234917015,
          1.0549312652219875,
          1.36121201935598,
          1.6517144085978883,
          1.9479459678253364,
          2.253380787979585,
          2.5406985707543126,
          2.8288417292864243,
          3.1235974378665317,
          3.404785308807161,
          3.686393098423363,
          3.9734070895377904,
          4.24947446088114,
          4.525114679277028,
          4.803821304103324,
          5.081124078841802,
          5.354843251199424,
          5.629153282026435,
          5.905654709798293,
          6.1805847588072975,
          6.458039682918237,
          6.735638786511495,
          7.015293552817844,
          7.295300354743993,
          7.575781706023804,
          7.857224626470109,
          8.136920484415251,
          8.415860337758605,
          8.698377916937957,
          8.972581163060369,
          9.245734698546478,
          9.527635078046034,
          9.802522133696957,
          10.077364894200452,
          10.356453842522031,
          10.63423918323383,
          10.90760730553423,
          11.18831155135763,
          11.476218192746636,
          11.758071208659235,
          12.047860819825235,
          12.345803509434328,
          12.640961374320227,
          12.941536761503569,
          13.243543379062109,
          13.541128701489344,
          13.847610044548075,
          14.154283866681745,
          14.463323969946268,
          14.787272714874067,
          15.11267581300668,
          15.44262188124273,
          15.786438787498332,
          16.134340167310306,
          16.476612757450123,
          16.827621450604358,
          17.183491532595667,
          17.531150826263314,
          17.887468419248233,
          18.250366537784384,
          18.603258103224125,
          18.95443092986873,
          19.315382663174475,
          19.673979602903874,
          20.02819178460713,
          20.398673367513535,
          20.771161872270007,
          21.1397403314832,
          21.518887519664364,
          21.890392100554525,
          22.26401380716324,
          22.642512051992497,
          23.020604647065987,
          23.398080979758404,
          23.781131794701917,
          24.16279834599238,
          24.54538941963393,
          24.925034022976934,
          25.301558341561474,
          25.682691242010932,
          26.06308178519438,
          26.441107240221204,
          26.823407454652976,
          27.211171095128275,
          27.5999302754471,
          27.982455200227168,
          28.361343680583293,
          28.74381713711348,
          29.123582215110392,
          29.488886270875092,
          29.862096056049598,
          30.241283770536587,
          30.60876348191735,
          30.97868120493982,
          31.36004238146997,
          31.745994525277986,
          32.15135014040447,
          32.564712558980936,
          32.9793444069204,
          33.38570310892224,
          33.79531811428434,
          34.20884110835389,
          34.61594856754298,
          35.02158154670799,
          35.42810542797403,
          35.82533851398963,
          36.20299150015205,
          36.576049237986034,
          36.949603448124485,
          37.32747549150403,
          37.694552580094026,
          38.05777027885687,
          38.42564998251778,
          38.78661261190079,
          39.13919620363345,
          39.48881580763127,
          39.823269953387324,
          40.1552476544533,
          40.48951364580601,
          40.8308380346881,
          41.169123505931374,
          41.50091361817909,
          41.82877954165472,
          42.161211761307214,
          42.53384607403117,
          42.85390103882031,
          43.190585475213666,
          43.53687048371664,
          43.8734460201353,
          44.206873986830985,
          44.54718352235755,
          44.88486527932402,
          45.22597486607037,
          45.55864806328055,
          45.89295706657062,
          46.23685371584923,
          46.578635342002485,
          46.96570251114636,
          47.30549813131491,
          47.647944107113084,
          48.0299351396432,
          48.37663105407652,
          48.723091223027645,
          49.06461095247348,
          49.40423309311393,
          49.73345353823621,
          50.05590173565162,
          50.38364087341626,
          50.69538798388635,
          51.01397427168325,
          51.33558879433273,
          51.641343886013566,
          51.951002026893995,
          52.24745270667296,
          52.52009976595814,
          52.79409336395465,
          53.056168776154074,
          53.29916197386721,
          53.542119577137356,
          53.77548751838303,
          53.98972566766802,
          54.19780608146605,
          54.40000101563082,
          54.58542908373879,
          54.76149985847198,
          54.933541685609974,
          55.09680317271314,
          55.25516648543737,
          55.404337880606256,
          55.55260192293612,
          55.70100143229448,
          55.84689530842236,
          55.98901658440931,
          56.1274801447216,
          56.266954479522866,
          56.398290155081085,
          56.52141291498931,
          56.639818795214296,
          56.75417643877159,
          56.86588439053571,
          56.97724895851334,
          57.08765418632386,
          57.194903490001494,
          57.302095010086965,
          57.4111502464549,
          57.52125196218386,
          57.63103824796659,
          57.74345404533255,
          57.85723979687369,
          57.96989623182933,
          58.082251173422755,
          58.193998337290665,
          58.30316282875393,
          58.41279646773634,
          58.52226490575659,
          58.62883440371537,
          58.733900490591566,
          58.83782226094718,
          58.93856533122835,
          59.03756024483546,
          59.135116845068765,
          59.23017499310952,
          59.32459931545914,
          59.41932113439755,
          59.510972975658966,
          59.601211201574046,
          59.689308873746064,
          59.77493653151537,
          59.85776452024836,
          59.941096147987736,
          60.02163587470475,
          60.10170195176904,
          60.18460267445845,
          60.263232971017366,
          60.33926511666251,
          60.41769819132252,
          60.495179538168934,
          60.570220558885225,
          60.64833769707762,
          60.73019306636724,
          60.81172843274648,
          60.89178449406931,
          60.97538424734452,
          61.05748686121893,
          61.136606124892936,
          61.216399925047156,
          61.293448043374816,
          61.36617121951862,
          61.43871449842724,
          61.510564895585645,
          61.57681795945674,
          61.64200146238275,
          61.70695730478563,
          61.76872440249366,
          61.82767457302494,
          61.88676427249198,
          61.943332805132165,
          61.99901608227632,
          62.05215932312734,
          62.103813847898344,
          62.15394203445875,
          62.201862856079764,
          62.24951191947457,
          62.29634182247722,
          62.34310520623603,
          62.39020576470519,
          62.438015061127025,
          62.48455579702712,
          62.530495442270784,
          62.57580279453953,
          62.62146665975984,
          62.667897127129066,
          62.71240911459497,
          62.753441841747254,
          62.79587534233998,
          62.83213741251281,
          62.864540001077366,
          62.892898865774384,
          62.9207419286591,
          62.94819145548893,
          62.97430483549647,
          62.99771545227248,
          63.02032406898697,
          63.043862817966506,
          63.065520088153946,
          63.08522345786388,
          63.10413648566231,
          63.12341713274369,
          63.13976962941787,
          63.15316861263422,
          63.16319691866358,
          63.16681037120316,
          63.16258576546753,
          63.15065501859352,
          63.13130205748566,
          63.10407062765513,
          63.069659479745,
          63.02757885766015,
          62.977488055501304,
          62.918935496376534,
          62.847733698542605,
          62.76560608451621,
          62.67557487074328,
          62.57220187688181,
          62.45885335213861,
          62.33653285337155,
          62.20024636437273,
          62.04708262626295,
          61.880802128259035,
          61.69602429674882,
          61.49496048924611,
          61.29084773812193,
          61.06874810301068,
          60.82581287630145,
          60.57639517485764,
          60.31534715831782,
          60.03931630033132,
          59.754994038584314,
          59.47036274404793,
          59.1715753454941,
          58.8625908398959,
          58.56693161420471,
          58.25656568451404,
          57.925795746722315,
          57.61280676055169,
          57.28595121383907,
          56.94111979189009,
          56.608454883131486,
          56.270588487932976,
          55.91067887127243,
          55.551892713296326,
          55.19792082565269,
          54.833086432303105,
          54.463140350791555,
          54.097272129762004,
          53.73312554031859,
          53.375446048491646,
          53.01450056636561,
          52.65013323361343,
          52.29745304089723,
          51.9502983136156,
          51.59424668940708,
          51.247238090189526,
          50.90315280372953,
          50.54905785577626,
          50.19696928216013,
          49.855216879994146,
          49.51076195171792,
          49.154018596198995,
          48.81857258633425,
          48.48865318120291,
          48.143320891553486,
          47.80972640693565,
          47.48871297119639,
          47.1512167145284,
          46.81997949432103,
          46.49637951304719,
          46.16083474483752,
          45.8274410700448,
          45.49846805089586,
          45.16070593469609,
          44.817721726843224,
          44.48321331151424,
          44.14153088138874,
          43.79062762329432,
          43.443213757129946,
          43.09318198656066,
          42.73562721602073,
          42.382947454964935,
          42.03219536972676,
          41.67843307535282,
          41.328529023447196,
          40.97344681645272,
          40.627303121565774,
          40.27364871945597,
          39.91782059955079,
          39.5640208647328,
          39.21084060759426,
          38.86200755971636,
          38.5055333369679,
          38.15261714586123,
          37.80319478493362,
          37.44814959969886,
          37.09327679201676,
          36.74140749230282,
          36.395768617004535,
          36.04201882293896,
          35.69140672805515,
          35.34625782172316,
          34.998131812084736,
          34.658060101582414,
          34.317091093958076,
          33.970542088840354,
          33.6356431092576,
          33.30204028703879,
          32.95188023809419,
          32.60846743182351,
          32.28153403172458,
          31.929165487454924,
          31.575270490308046,
          31.242567646197134,
          30.899120391448676,
          30.545351229558054,
          30.21400816570368,
          29.88511266633807,
          29.534345705160842,
          29.19952034673891,
          28.867191193189598,
          28.529758972681886,
          28.191057625758333,
          27.858915026211122,
          27.526308181645305,
          27.190103794311515,
          26.849015263509017,
          26.51499068605483,
          26.190509471998876,
          25.85229131803252,
          25.521173501037953,
          25.196906729390108,
          24.872561950203373,
          24.540782558185178,
          24.22042256237104,
          23.90379147736523,
          23.580770986210098,
          23.259193605999087,
          22.928224860142095,
          22.592313515169423,
          22.25120512719226,
          21.911808214257647,
          21.56848348644662,
          21.221891796361295,
          20.883161507515446,
          20.535772971541892,
          20.18594869984632,
          19.840256311549158,
          19.522894062647886,
          19.221767428364362,
          18.916869370600157,
          18.610694419625357,
          18.304527120903813,
          17.998193376915065,
          17.68614497829255,
          17.368374003372246,
          17.055898032511053,
          16.742428610601262,
          16.395708258790776,
          16.047696883677325,
          15.700350034610413,
          15.342330962379123,
          14.996353855710264,
          14.65303434823042,
          14.288252134843123,
          13.940287211306334,
          13.602940410547475,
          13.234047716816413,
          12.896610716579785,
          12.588389358956583,
          12.252416432126967,
          11.918681419217677,
          11.597451551881075,
          11.263986521165688,
          10.922164135037553,
          10.59205226676616,
          10.260804067987845,
          9.924129373158884,
          9.581488140247956,
          9.238636738886148,
          8.892296718298766,
          8.543953044630854,
          8.19932896820383,
          7.847807479737154,
          7.500880523391266,
          7.149134410768912,
          6.800151472885508,
          6.458298987676256,
          6.067467643415407,
          5.6663057329743864,
          5.264503893602143,
          4.8572832148179215,
          4.453235721366303,
          4.053094547937241,
          3.652960086725024,
          3.2470833617517623,
          2.8377152466977327,
          2.442170781170606,
          2.0733639653890075,
          1.7121062176798152,
          1.3553154484853542,
          1.008120248677175,
          0.6531759357421323,
          0.2957001583769022,
          -0.045588823825584934,
          -0.39040236296740793,
          -0.7365156575763289,
          -1.0759587364390546,
          -1.42765018385535,
          -1.7810083058053876,
          -2.132145207433067,
          -2.487960236796579,
          -2.8473526621413052,
          -3.1894780564959735,
          -3.541628825093142,
          -3.9018145842456127,
          -4.244464990438296,
          -4.597772037326932,
          -4.938988118005556,
          -5.259683603972067,
          -5.586728562499185,
          -5.918260677472239,
          -6.238395573807465,
          -6.555802078373068,
          -6.879731327802897,
          -7.191564412808025,
          -7.505322713276001,
          -7.813143843720128,
          -8.10568855883533,
          -8.403458055589457,
          -8.691535697206799,
          -8.96512686888636,
          -9.232974116072883,
          -9.495618210597758,
          -9.751710520551049,
          -9.995911282781275,
          -10.234816636036385,
          -10.466279546186946,
          -10.691092941439853,
          -10.909667557359215,
          -11.118302880163718,
          -11.322286401467391,
          -11.516752150838526,
          -11.696961868980662,
          -11.868592194147638,
          -12.029254118218732,
          -12.169693663933018,
          -12.288543113346856,
          -12.396469529359633,
          -12.48652212662586,
          -12.552545055998337,
          -12.59818074208725,
          -12.624269391935025,
          -12.629106635940238,
          -12.614101957322276,
          -12.577234483587432,
          -12.520041035001883,
          -12.442057338132571,
          -12.339029238408774,
          -12.228663788046836,
          -12.097357603808792,
          -11.948131239600722,
          -11.782771255608534,
          -11.599891594303266,
          -11.40369688475966,
          -11.196285598363788,
          -10.97561484954418,
          -10.742889917127997,
          -10.495056045696266,
          -10.239725653017821,
          -9.971596647763095,
          -9.69362709385564,
          -9.411177411156174,
          -9.118580270417132,
          -8.822237366562877,
          -8.524324944016028,
          -8.217322449982737,
          -7.910114178832905,
          -7.601505598627543,
          -7.284268983769043,
          -6.9686018967643735,
          -6.653185389937518,
          -6.331826886778154,
          -6.010864554039517,
          -5.690842623903828,
          -5.371808261193764,
          -5.054195012682517,
          -4.733805838736679,
          -4.416618655951184,
          -4.10299996747427,
          -3.788231790806858,
          -3.473462289396849,
          -3.160723804066829,
          -2.8480700036458626,
          -2.538085486383813,
          -2.2298726158062685,
          -1.9203394273430623,
          -1.6213310265684997,
          -1.3227658015797874,
          -1.0184324606870485,
          -0.7249762027226001,
          -0.4322715980699082,
          -0.14508058340152255,
          0.15235075104773366,
          0.4419773073619327,
          0.7171089936424838,
          1.0054662364139046,
          1.2892299372113842,
          1.5605599943474036,
          1.8373176021811874,
          2.1208128844037812,
          2.3930942708221936,
          2.661157093171031,
          2.9351009213663573,
          3.2013135802439643,
          3.46178745605126,
          3.726781028256172,
          3.9861202558622395,
          4.237716202058085,
          4.492567951177932,
          4.741130887136513,
          4.993463675497179,
          5.245831451551488,
          5.495833298364509,
          5.74944512382775,
          6.00536853669388,
          6.260677354889801,
          6.513063815117789,
          6.770365841426887,
          7.023898623723458,
          7.276124508341358,
          7.531558524567593,
          7.784017237435444,
          8.034259964974401,
          8.284689138222124,
          8.535342159440725,
          8.779928423684392,
          9.030426110527335,
          9.283448483197963,
          9.529826705558682,
          9.786024332313293,
          10.041049836365245,
          10.293593384284025,
          10.55281780802128,
          10.81738048985599,
          11.088002760129802,
          11.35617748549179,
          11.631303476708556,
          11.919522587916266,
          12.207777129396131,
          12.504517114288772,
          12.804301013902991,
          13.101980739751278,
          13.409195325961342,
          13.720499712703655,
          14.036892550655365,
          14.362011516524657,
          14.695609050562826,
          15.031900523752672,
          15.38259496943098,
          15.73981525956396,
          16.09709122612972,
          16.46417458246968,
          16.835838019024283,
          17.206555908693492,
          17.57279411182098,
          17.991427406425363,
          18.372803663965243,
          18.746692056133323,
          19.130651942000195,
          19.52018427367376,
          19.900199475698994,
          20.28545860993254,
          20.674789782189027,
          21.059827285836285,
          21.441772860971263,
          21.827496927549927,
          22.211904051257765,
          22.59551358289561,
          22.979273351188308,
          23.363501395093923,
          23.744613641519187,
          24.126580476455306,
          24.504983215049606,
          24.88230034185392,
          25.258633532933196,
          25.63812818572565,
          26.01412035014803,
          26.39250284579615,
          26.767103944085427,
          27.146009381300964,
          27.51170048987215,
          27.87410896255844,
          28.241952288576122,
          28.602691943464166,
          28.95355977046983,
          29.313446394771386,
          29.668189436415958,
          30.015513608150005,
          30.360145692133205,
          30.698401782550082,
          31.035309387674015,
          31.355796543763514,
          31.674132913036836,
          31.99673504156595,
          32.31082093979031,
          32.62140843180969,
          32.92821709329264,
          33.229568166137355,
          33.525258079597634,
          33.79812562467964,
          34.06653626079953,
          34.321557028165536,
          34.55231789168267,
          34.78432485260065,
          34.998310715271934,
          35.197683409277694,
          35.3938340601963,
          35.5725446714508,
          35.731257533845074,
          35.89134601101259,
          36.03495718213001,
          36.15892083376345,
          36.28134096300529,
          36.389296709138954,
          36.48105293487644,
          36.56944746692986,
          36.64455672695461,
          36.71000569805783,
          36.76410075508549,
          36.80649007590402,
          36.84359396210188,
          36.875750921106814,
          36.902926290955435,
          36.92854379253948,
          36.95410207191664,
          36.98011036055201,
          37.00537275589032,
          37.01320860167798,
          37.01985694270312,
          37.025749134491626,
          37.03169101143714,
          37.03688238596416,
          37.041405491709455,
          37.045811110102896,
          37.04987485131563,
          37.0534028622793,
          37.056311229292355,
          37.08321001137313,
          37.11314971410027,
          37.143528791302856,
          37.17446579043236,
          37.20591960279453,
          37.237896668859186,
          37.27040584185612,
          37.303362114184154,
          37.33723189714945,
          37.371875566971745,
          37.38034051641658,
          37.38583697011502,
          37.391522477780526,
          37.39717013777862,
          37.40280510310003,
          37.40858299711785,
          37.41430185704812,
          37.4200672221251,
          37.42589436129573,
          37.4317431418861,
          37.45154482485271,
          37.472932469680785,
          37.494409422589015,
          37.51584461079809,
          37.537293522947095,
          37.55875868362723,
          37.58020758034309,
          37.6016794688646,
          37.623156909146495,
          37.64470476223522,
          37.65231583624131,
          37.65853359551304,
          37.66481328947362,
          37.67100918601555,
          37.677132190172806,
          37.683396930808506,
          37.689682498981604,
          37.69590200806786,
          37.70226605813416,
          37.70857938006345,
          37.74377347336275,
          37.782708193364776,
          37.82160512511236,
          37.86032954299645,
          37.89879756115578,
          37.937202991114304,
          37.975692103694485,
          38.013981789777695,
          38.05207367964482,
          38.09055529940335,
          38.09868021371338,
          38.10333396589485,
          38.10787050330368,
          38.112195856538385,
          38.11651440069659,
          38.12081101898356,
          38.12515539439644,
          38.12996653572406,
          38.13438467616609,
          38.138710648102204,
          38.13987763102785,
          38.140980726973915,
          38.14190973106088,
          38.14284673668466,
          38.143966100564406,
          38.1450411963866,
          38.14602135520899,
          38.14704642208374,
          38.14814007552123
         ]
        },
        {
         "marker": {
          "color": "red",
          "size": 8,
          "symbol": "star"
         },
         "mode": "markers",
         "name": "Landmarks",
         "type": "scatter",
         "x": [
          -48.11741249184751,
          -80.9281129508125,
          -47.60339748000676,
          -17.70157972379622
         ],
         "y": [
          31.924679924108325,
          53.95372590607549,
          -19.972945092661757,
          66.35356579052397
         ]
        }
       ],
       "layout": {
        "legend": {
         "tracegroupgap": 0,
         "x": 0.01,
         "xanchor": "left",
         "y": 0.99,
         "yanchor": "top"
        },
        "margin": {
         "b": 20,
         "l": 20,
         "r": 20,
         "t": 40
        },
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             },
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "pattern": {
              "fillmode": "overlay",
              "size": 10,
              "solidity": 0.2
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "fillpattern": {
             "fillmode": "overlay",
             "size": 10,
             "solidity": 0.2
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "autotypenumbers": "strict",
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Plaza2 Batch SLAM Result"
        },
        "xaxis": {
         "anchor": "y",
         "domain": [
          0,
          1
         ],
         "title": {
          "text": "X (m)"
         }
        },
        "yaxis": {
         "anchor": "x",
         "domain": [
          0,
          1
         ],
         "scaleanchor": "x",
         "scaleratio": 1,
         "title": {
          "text": "Y (m)"
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot using Plotly (similar to iSAM example)\n",
    "fig = px.line(x=positions_initial[:,0], y=positions_initial[:,1], title='Plaza2 Batch SLAM Result')\n",
    "fig.data[0].name = 'Initial (Odometry)'\n",
    "fig.data[0].showlegend = True\n",
    "fig.data[0].line.color = 'orange'\n",
    "fig.data[0].line.dash = 'dash'\n",
    "\n",
    "fig.add_scatter(x=positions_result[:,0], y=positions_result[:,1], mode='lines', \n",
    "                line=dict(color='black'), name='Optimized Path')\n",
    "\n",
    "fig.add_scatter(x=landmarks_result[:,0], y=landmarks_result[:,1], mode='markers', \n",
    "                marker=dict(color='red', symbol='star', size=8), name='Landmarks')\n",
    "\n",
    "# Configure layout\n",
    "fig.update_layout(margin=dict(l=20, r=20, t=40, b=20), \n",
    "                  legend=dict(yanchor=\"top\", y=0.99, xanchor=\"left\", x=0.01),\n",
    "                  xaxis_title=\"X (m)\", yaxis_title=\"Y (m)\")\n",
    "fig.update_yaxes(scaleanchor=\"x\", scaleratio=1) # Ensure aspect ratio is 1:1\n",
    "fig.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py312",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.6"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
